Combinatorics : the Rota way

Joseph P.S. Kung, Gian-Carlo Rota, Catherine H. Yan

Gian-Carlo Rota was one of the most original and colourful mathematicians of the 20th century. His work on the foundations of combinatorics focused on the algebraic structures that lie behind diverse combinatorial areas, and created a new area of algebraic combinatorics. Written by two of his former students, this book is based on notes from his influential graduate courses and on face-to-face discussions. 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 linear lattices, modular and geometric lattices, valuation rings, generating functions, umbral calculus, symmetric functions, Baxter algebras, unimodality of sequences, and location of zeros of polynomials. Many exercises and research problems are included, and unexplored areas of possible research are discussed. A must-have for all students and researchers in combinatorics and related areas.

「Nielsen BookData」より

Gian-Carlo Rota was one of the most original and colourful mathematicians of the 20th century. His work on the foundations of combinatorics focused on the algebraic structures that lie behind diverse combinatorial areas, and created a new area of algebraic combinatorics. Written by two of his former students, this book is based on notes from his influential graduate courses and on face-to-face discussions. 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 linear lattices, modular and geometric lattices, valuation rings, generating functions, umbral calculus, symmetric functions, Baxter algebras, unimodality of sequences, and location of zeros of polynomials. Many exercises and research problems are included, and unexplored areas of possible research are discussed. A must-have for all students and researchers in combinatorics and related areas.

「Nielsen BookData」より

[目次]

  • 1. Sets, functions, and relations
  • 2. Matching theory
  • 3. Partially ordered sets and lattices
  • 4. Generating functions and the umbral calculus
  • 5. Symmetric functions and Baxter algebras
  • 6. Determinants, matrices, and polynomials
  • 7. Selected solutions.

「Nielsen BookData」より

[目次]

  • 1. Sets, functions, and relations
  • 2. Matching theory
  • 3. Partially ordered sets and lattices
  • 4. Generating functions and the umbral calculus
  • 5. Symmetric functions and Baxter algebras
  • 6. Determinants, matrices, and polynomials
  • 7. Selected solutions.

「Nielsen BookData」より

この本の情報

書名 Combinatorics : the Rota way
著作者等 Kung, Joseph P. S.
Rota, Gian-Carlo
Yan Catherine H.
出版元 Cambridge University Press
刊行年月 2009
ページ数 xii, 396 p.
大きさ 24 cm
ISBN 9780521737944
9780521883894
NCID BA89184530
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言語 英語
出版国 イギリス
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