Combinatorics of Set Partitions

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CRC Press, 27 de jul. 2012 - 516 pàgines

Focusing on a very active area of mathematical research in the last decade, Combinatorics of Set Partitions presents methods used in the combinatorics of pattern avoidance and pattern enumeration in set partitions. Designed for students and researchers in discrete mathematics, the book is a one-stop reference on the results and research activities of set partitions from 1500 A.D. to today.

Each chapter gives historical perspectives and contrasts different approaches, including generating functions, kernel method, block decomposition method, generating tree, and Wilf equivalences. Methods and definitions are illustrated with worked examples and MapleTM code. End-of-chapter problems often draw on data from published papers and the author’s extensive research in this field. The text also explores research directions that extend the results discussed. C++ programs and output tables are listed in the appendices and available for download on the author’s web page.

 

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Combinatorics of Set Partitions
Toufik Mansour
Previsualització limitada - 2012

Frases i termes més freqüents

algorithm alphabet asymptotic Bell numbers Belln bijection boson cells Chapter column combinatorial completes the proof contains Corollary define Definition derive Discrete Math Dyck paths elements enumeration equivalent exactly k blocks Example Exercise explicit formula exponential generating function Ferrers diagram Feynman diagram find find an explicit first following result given gives Gray code implies initial conditions integer Lemma letter linear representation logn Mansour n-th noncrossing partitions noncrossing set partitions nonempty Note number of blocks number of occurrences number of set obtain ordinary generating function partitions of n partitions of Pn,k pattern avoidance permutations polynomial polyomino Proof Let Proposition q-analog recurrence relation Research Direction rook placement satisfies second kind sequence set partition 71 Shattuck statistics on set Stir(n Stir(n,k Stirling numbers subsequence pattern subset subword pattern Theorem tion total number weak records Wilf-equivalence

Sobre l'autor (2012)

Toufik Mansour is a professor in the Department of Mathematics at the University of Haifa. Dr. Mansour has authored/co-authored more than 200 papers and is a reviewer for many journals, including Advances in Applied Mathematics, Discrete Mathematics, Discrete Applied Mathematics, European Journal of Combinatorics, and the Journal of Combinatorial Theory Series A. His research focuses on pattern avoidance in permutations, colored permutations, set partitions, words, and compositions.

Informació bibliogràfica

TítolCombinatorics of Set Partitions
Discrete Mathematics and Its Applications
AutorToufik Mansour
Edicióil·lustrada
EditorCRC Press, 2012
ISBN1439863334, 9781439863336
Nre. de pàgines516 pàgines
  
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