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Combinatorics: The Rota Way - Joseph P. S. Kung, Gian-Carlo Rota, Catherine H. Yan

Combinatorics: The Rota Way

Buch | Hardcover
408 Seiten
2009
Cambridge University Press (Verlag)
978-0-521-88389-4 (ISBN)
CHF 189,95 inkl. MwSt
Gian-Carlo Rota was one of the most original and colourful mathematicians of the twentieth century. His work on the foundations of combinatorics created a new area of algebraic combinatorics. The book is based upon his influential graduate courses on the foundations of combinatorics, that have influenced generations of students.
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.

Dr Joseph P. S. Kung is Professor of Mathematics at the University of North Texas. He is currently an editor-in-chief for the journal Advances in Applied Mathematics. Gian-Carlo Rota (1932–1999) was a Professor of Applied Mathematics and Natural Philosophy at the Massachusetts Institute of Technology. He was a member of the National Academy of Science. He was awarded the 1988 Steele Prize of the American Mathematical Society for his 1964 paper 'On the Foundations of Combinatorial Theory I. Theory of Moebius Functions.' He was the founding editor of the Journal of Combinatorial Theory. Catherine H. Yan is a Professor of Mathematics at Texas A & M University. She was a Courant Instructor at New York University (1997–1999) and a Sloan Fellow (2001–2003).

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.

Erscheint lt. Verlag 9.2.2009
Reihe/Serie Cambridge Mathematical Library
Zusatzinfo Worked examples or Exercises; 3 Line drawings, unspecified
Verlagsort Cambridge
Sprache englisch
Maße 157 x 235 mm
Gewicht 650 g
Themenwelt Mathematik / Informatik Mathematik Graphentheorie
ISBN-10 0-521-88389-X / 052188389X
ISBN-13 978-0-521-88389-4 / 9780521883894
Zustand Neuware
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