Wilf H.S. Lectures on Integer Partitions

Dover Publications, 2002. - 272 pages. Coherent treatment provides comprehensive view of basic methods and results of the combinatorial study of finite set systems. The Clements-Lindstrom extension of the Kruskal-Katona theorem to multisets is explored, as is the Greene-Kleitman result concerning k-saturated chain partitions of general partially ordered sets. Connections with Dilworth's theorem, the marriage problem, and probability are also dis...

Springer, 2008. - 314 pages. The main focus of these lectures is basis extremal problems and inequalities – two sides of the same coin. Additionally they prepare well for approaches and methods useful and applicable in a broader mathematical context. Highlights of the book include a solution to the famous 4m-conjecture of Erd?s/Ko/Rado 1938, one of the oldest problems in combinatorial extremal theory, an answer to a question of Erd?s (1962) in c...

Centre de Recherches Math?matiques, Montr?al, 2008, -202 pp. This book grew out of two series of five two-hour lectures, given by Jean Berstel and Christophe Reutenauer in March 2007. Notes for the lectures were written down by Aaron Lauve and Franco Saliola. They have augmented their notes with several topics and have added more than 100 exercises. There has been a lot of work in adding bibliographic references and a detailed index. The text is...

Издательство IOS Press, 2011, -460 pp. This book contains papers based on lectures presented at the NATO Advanced Study Institute "Information Security and Related Combinatorics", held in the beautiful town of Opatija at the Adriatic Coast of Croatia from May 31 to June 11, 2010. On behalf of all participants, we would like to thank the NATO Science for Peace and Security Programme for providing funds for the conference, as well as the local spo...

M. Dekker, 1999. - 308 pages. Thoroughly revised, updated, expanded, and reorganized to serve as a primary text for mathematics courses, Introduction to Set Theory, Third Edition covers the basics: relations, functions, orderings, finite, countable, and uncountable sets, and cardinal and ordinal numbers. It also provides five additional self-contained chapters, consolidates the material on real numbers into a single updated chapter affording fle...

Издательство Springer, 2010, -366 pp. This book is the second volume of mathematical papers to commemorate the 60th birthday of Laszlo ('Laci') Lovasz on March 9, 2008. Prominent mathematicians that were inspired by Laci were invited to contribute to the celebrations of this milestone in the Summer of 2008. The response was overwhelming, and therefore two conferences were organized , the first from 5-9 August 2008 in Budapest, and the second the...

Cambridge University Press, 2009. - 408 pages. Written by two of Gian-Carlo Rota's former students, this book is based on notes from his courses and on personal discussions with him. Topics include sets and valuations, partially ordered sets, distributive lattices, partitions and entropy, matching theory, free matrices, doubly stochastic matrices, Moebius functions, chains and antichains, Sperner theory, commuting equivalence relations and linea...

Kapa & Omega, Glendale, AZ, USA, 2010. - 503 p. Abstract: A Smarandache system (G;R) is such a mathematical system with at least one Smarandachely denied rule r in R such that it behaves in at least two different ways within the same set G, i.e. , validated and invalided, or only invalided but in multiple distinct ways. A map is a 2-cell decomposition of surface, which can be seen as a connected graphs in development from partition to permuta...

Издательство Academic Press, 1978, -316 pp. Описан набор эффективных по скорости и памяти комбинаторных алгоритмов. Содержит подробное описание алгоритмов и код на Фортране. Combinatorial families. Next Subset of an n-Set. Random Subset of an n-Set. Next k-Subset of an n-Set. Random k-Subset of an n-Set. Next Composition of n into k Parts. Random Composition of n into k Parts. Next Permutation of n Letters. Random Permutation of n Letters. Next P...

A K Peters, 2006. - 245 pages. Generating functions, one of the most important tools in enumerative combinatorics, are a bridge between discrete mathematics and continuous analysis. Generating functions have numerous applications in mathematics, especially in. * Combinatorics. * Probability Theory. * Statistics. * Theory of Markov Chains. * Number Theory. One of the most important and relevant recent applications of combinatorics lies in th...