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题名/责任者:

Stirling numbers / Elena Deza, Moscow State Pedagogical University, Russia.

出版发行项:

New Jersey (Hackensack) : World Scientific, 2024.

ISBN:

9789811278099:

载体形态项:

xxvii, 438 pages : illustrations ; 24 cm

丛编说明:

Selected Chapters of Number Theory: Special Numbers ; volume 3

个人责任者:

Deza, Elena, author.

论题主题:

Stirling numbers.

中图法分类号:

O151.1

书目附注:

Includes bibliographical references and index.

摘要附注:

"Stirling numbers are one of the most known classes of special numbers in Mathematics, especially in Combinatorics and Algebra. They were introduced by Scottish mathematician James Stirling (1692-1770) in his most important work, Differential Method with a Tract on Summation and Interpolation of Infinite Series (1730). Stirling numbers have rich history; many arithmetic, number-theoretical, analytical and combinatorial connections; numerous classical properties; as well as many modern applications. This book collects together much of the scattered material on the two subclasses of Stirling numbers to provide a holistic overview of the topic. From the combinatorial point of view, Stirling numbers of the second kind S(n,k) count the number of ways to partition a set of n different objects (i.e., a given n-set) into k non-empty subsets. Stirling numbers of the first kind s(n, k) give the number of permutations of n elements with k disjoint cycles. Both subclasses of Stirling numbers play an important role in Algebra: they form the coefficients, connecting well-known sets of polynomials. This book is suitable for students and professionals, providing a broad perspective of the theory of this class of special numbers, and many generalizations and relatives of Stirling numbers, including Bell numbers and Lah numbers. Throughout the book, readers are presented with exercises to test and cement their understanding"--

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