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Combinatorics and Number Theory of Counting Sequences

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Combinatorics and Number Theory of Counting Sequences

4.85 41,590 ratings · 3,675 reviews
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Overview: Combinatorics and Number Theory of Counting Sequences is an introduction to the theory of finite set partitions and to the enumeration of cycle decompositions of permutations.The presentation prioritizes elementary enumerative proofs. Therefore, parts of the book are designed so that even those high school students and teachers who are interested in combinatorics can have the benefit of them. Still, the book collects vast, up-to-date information for many counting sequences (especially, related to set partitions and permutations), so it is a must-have piece for those mathematicians who do research on enumerative combinatorics.In addition, the book contains number theoretical results on counting sequences of set partitions and permutations, so number theorists who would like to see nice applications of their area of interest in combinatorics will enjoy the book, too. FeaturesThe Outlook sections at the end of each chapter guide the reader towards topics not covered in the book, and many of the Outlook items point towards new research problems.An extensive bibliography and tables at the end make the book usable as a standard reference.Citations to results which were scattered in the literature now become easy, because huge parts of the book (especially in parts II and III) appear in book form for the first time.

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Istvan Mezo
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Istvan Mezo
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Istvan Mezo writes contemporary fiction and has always been fascinated by character-driven stories. They hold a degree in English Literature and previously worked as an editor before transitioning to writing their own books. Istvan Mezo lives with their spouse and a very vocal rescue cat.

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Joseph Walker
Joseph Walker March 20, 2024
Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. A true literary gem.
Betty Torres
Betty Torres December 07, 2024
I thoroughly enjoyed the elegance of it. It held my rapt attention, even when certain twists were telegraphed. A solid 4 stars from me.
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Laura Carter July 04, 2024
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Brian Thompson January 21, 2024
I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. A very distinguished novel.
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A profoundly satisfying read. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
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Michael Garcia November 02, 2024
A highly sophisticated read. It held my rapt attention, even when certain twists were telegraphed. I would highly recommend this to discerning readers.
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Robert Lee October 04, 2024
I thoroughly enjoyed the elegance of it. It held my rapt attention, even when certain twists were telegraphed. Quite impressive overall.
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Laura Green November 10, 2025
Took a moment to build, but the payoff was spectacular. It held my rapt attention, even when certain twists were telegraphed. A very distinguished novel.
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Donald Taylor August 30, 2024
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Emily Sanchez
Emily Sanchez May 09, 2025
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Anthony Robinson
Anthony Robinson July 05, 2024
Excellent, though slightly flawed. It held my rapt attention, even when certain twists were telegraphed. A very distinguished novel.
David Turner
David Turner May 10, 2025
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Michael Williams November 22, 2025
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Nicholas Evans May 21, 2025
Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
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Kevin Phillips July 22, 2025
Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
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An acceptable diversion. The prose was competent, yet the characters lacked the depth I usually seek. Perhaps more aligned with a different audience's tastes.
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Took a moment to build, but the payoff was spectacular. It held my rapt attention, even when certain twists were telegraphed. A very distinguished novel.
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Laura Gonzalez October 02, 2025
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I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. Quite impressive overall.
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Michelle Carter
Michelle Carter January 28, 2024
Not entirely to my refined tastes. The prose was competent, yet the characters lacked the depth I usually seek. Perhaps more aligned with a different audience's tastes.
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A highly sophisticated read. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. I would highly recommend this to discerning readers.
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Nicholas Evans April 16, 2025
I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. A wonderful companion for a quiet weekend.
Rebecca Young
Rebecca Young June 30, 2024
Such a rich narrative. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
David Lopez
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Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
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Took a moment to build, but the payoff was spectacular. It held my rapt attention, even when certain twists were telegraphed. A very distinguished novel.
James Jackson
James Jackson June 08, 2024
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A profoundly satisfying read. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
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A highly sophisticated read. It held my rapt attention, even when certain twists were telegraphed. I would highly recommend this to discerning readers.
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A highly sophisticated read. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. Quite impressive overall.
Barbara Cruz
Barbara Cruz June 13, 2025
Such a rich narrative. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading.
Jacob Wilson
Jacob Wilson September 18, 2025
I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. A solid 4 stars from me.
Steven Young
Steven Young December 28, 2024
A very strong entry. The middle had a deliberate pace, but the climax was phenomenal. Quite impressive overall.
Margaret Sanchez
Margaret Sanchez November 25, 2024
Took a moment to build, but the payoff was spectacular. The middle had a deliberate pace, but the climax was phenomenal. A very distinguished novel.
Brian Thompson
Brian Thompson March 08, 2025
A very strong entry. It held my rapt attention, even when certain twists were telegraphed. Quite impressive overall.
Ashley Brown
Ashley Brown March 13, 2024
Excellent, though slightly flawed. The protagonist was compelling, though some subplots felt slightly overshadowed. Quite impressive overall.
Donald Taylor
Donald Taylor May 19, 2025
I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
Jennifer Clark
Jennifer Clark April 06, 2025
Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
Steven Miller
Steven Miller August 31, 2024
A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
Edward  Parker
Edward Parker November 12, 2024
I thoroughly enjoyed the elegance of it. The middle had a deliberate pace, but the climax was phenomenal. Quite impressive overall.
Patricia Lewis
Patricia Lewis November 21, 2024
Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I am now a lifelong fan of this author.
Donald Adams
Donald Adams October 04, 2025
Honestly one of the most premium reading experiences lately. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
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Deborah Allen December 15, 2024
Honestly one of the most premium reading experiences lately. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author.
Daniel Diaz
Daniel Diaz April 06, 2024
Excellent, though slightly flawed. The middle had a deliberate pace, but the climax was phenomenal. A solid 4 stars from me.
Jennifer Williams
Jennifer Williams November 22, 2024
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Amanda Nelson
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Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
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Thomas Adams February 02, 2024
Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
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Jacob Sanchez January 05, 2025
Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
Andrew Turner
Andrew Turner July 12, 2025
Honestly one of the most premium reading experiences lately. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
Anthony Adams
Anthony Adams April 11, 2024
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Ashley Baker
Ashley Baker May 01, 2024
Exceeded all my expectations. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading.
James Sanchez
James Sanchez October 02, 2025
Took a moment to build, but the payoff was spectacular. It held my rapt attention, even when certain twists were telegraphed. I would highly recommend this to discerning readers.
Rebecca Young
Rebecca Young February 08, 2024
Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
Michael Hill
Michael Hill October 28, 2024
An acceptable diversion. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Perfectly average.
Thomas Adams
Thomas Adams November 19, 2025
Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
Richard Anderson
Richard Anderson June 02, 2024
Honestly one of the most premium reading experiences lately. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
Kevin Thompson
Kevin Thompson June 19, 2025
Such a rich narrative. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
Jessica Phillips
Jessica Phillips May 01, 2025
Honestly one of the most premium reading experiences lately. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An absolute must-read for connoisseurs of the genre.
Jessica Robinson
Jessica Robinson June 09, 2025
A profoundly satisfying read. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading.
Sarah Rodriguez
Sarah Rodriguez January 18, 2025
Took a moment to build, but the payoff was spectacular. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend.
Rebecca  Davis
Rebecca Davis May 09, 2025
I find myself somewhat conflicted. It verged on repetitive in the second act. A more concise edit would have served it well. Perhaps more aligned with a different audience's tastes.
Jennifer Hill
Jennifer Hill March 07, 2025
A very strong entry. A brilliant concept executed with flair. Just a few pacing choices I would change. A solid 4 stars from me.
Kimberly Rivera
Kimberly Rivera December 21, 2025
Took a moment to build, but the payoff was spectacular. It held my rapt attention, even when certain twists were telegraphed. A very distinguished novel.
Jennifer Sanchez
Jennifer Sanchez October 16, 2025
A highly sophisticated read. It held my rapt attention, even when certain twists were telegraphed. I would highly recommend this to discerning readers.
Joseph Lewis
Joseph Lewis March 15, 2024
Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
Betty Robinson
Betty Robinson August 29, 2025
Such a rich narrative. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
Richard Martinez
Richard Martinez December 17, 2025
Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An absolute must-read for connoisseurs of the genre.
Emily Sanchez
Emily Sanchez February 25, 2025
Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
Susan Wright
Susan Wright January 15, 2024
Excellent, though slightly flawed. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A wonderful companion for a quiet weekend.
Gary Scott
Gary Scott September 16, 2025
A highly sophisticated read. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A wonderful companion for a quiet weekend.
John  Parker
John Parker November 08, 2024
Honestly one of the most premium reading experiences lately. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
Andrew Wilson
Andrew Wilson July 17, 2024
Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
Rebecca Martinez
Rebecca Martinez September 16, 2024
Not entirely to my refined tastes. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. Unlikely to reread, but a reasonable expenditure of time.
Barbara Walker
Barbara Walker October 07, 2024
A very strong entry. A brilliant concept executed with flair. Just a few pacing choices I would change. Quite impressive overall.
Cynthia Clark
Cynthia Clark April 12, 2024
A very strong entry. The protagonist was compelling, though some subplots felt slightly overshadowed. A very distinguished novel.
Melissa Rodriguez
Melissa Rodriguez May 26, 2025
Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
Michelle Walker
Michelle Walker November 03, 2024
I thoroughly enjoyed the elegance of it. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. I would highly recommend this to discerning readers.
Matthew Gomez
Matthew Gomez November 07, 2025
Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author.
Melissa Edwards
Melissa Edwards March 23, 2024
Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
David Harris
David Harris March 31, 2024
Such a rich narrative. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
Ashley Torres
Ashley Torres July 02, 2024
I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
Michelle White
Michelle White April 16, 2024
Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author.
Eric Smith
Eric Smith June 18, 2025
I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
Thomas Lewis
Thomas Lewis September 26, 2025
A profoundly satisfying read. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An absolute must-read for connoisseurs of the genre.
Sandra Gomez
Sandra Gomez January 22, 2024
I thoroughly enjoyed the elegance of it. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A very distinguished novel.
Barbara  Davis
Barbara Davis March 08, 2025
A profoundly satisfying read. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
Edward Jackson
Edward Jackson January 19, 2024
Exceeded all my expectations. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
Richard Thomas
Richard Thomas April 29, 2024
Took a moment to build, but the payoff was spectacular. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend.
Robert Robinson
Robert Robinson January 06, 2025
Took a moment to build, but the payoff was spectacular. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. Quite impressive overall.
Jessica Williams
Jessica Williams August 24, 2025
I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
Charles Clark
Charles Clark June 01, 2025
I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading.
Jennifer Lee
Jennifer Lee May 03, 2025
Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading.
Stephanie Rodriguez
Stephanie Rodriguez November 22, 2025
Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
Michael Adams
Michael Adams September 14, 2024
Not entirely to my refined tastes. Certain acts were fascinating, while others felt like a slight endeavor to complete. A fair 3 stars.
Sharon Johnson
Sharon Johnson October 19, 2024
Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
Ashley Carter
Ashley Carter August 08, 2024
Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
Charles Diaz
Charles Diaz October 09, 2025
I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An absolute must-read for connoisseurs of the genre.
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