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Combinatorics : = the Rota way /

Rota, Gian-Carlo, (1932-1999.)

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Combinatorics : = the Rota way /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Combinatorics :/ Joseph P.S. Kung, Gian-Carlo Rota, Catherine H. Yan.
其他題名:	the Rota way /
作者:	Kung, Joseph P. S.
其他作者:	Rota, Gian-Carlo,
出版者:	Cambridge, UK ;Cambridge University Press, : 2009.,
面頁冊數:	xii, 396 p. :ill. ;24 cm.
叢書名:	Cambridge mathematical library
標題:	Combinatorial analysis. -
ISBN:	9780521883894 :

Combinatorics : = the Rota way /
Kung, Joseph P. S.

Combinatorics :the Rota way /Joseph P.S. Kung, Gian-Carlo Rota, Catherine H. Yan. - Cambridge, UK ;Cambridge University Press,2009. - xii, 396 p. :ill. ;24 cm. - Cambridge mathematical library. - Cambridge mathematical library..

Includes bibliographical references (p. 369-388) and index.

Sets, Functions, and Relations. Sets, valuations, and Boolean algebras --

Gian-Carlo Rota was one of the most original and colourful mathematicians of the 20th century. Written by two of his former students, this book is based on notes from his influential graduate courses and on face-to-face discussions.

ISBN: 9780521883894 :US99.00

LCCN: 2008037803

Nat. Bib. No.: GBA906361bnb

Nat. Bib. Agency Control No.: 014883716UkSubjects--Topical Terms:

523878
Combinatorial analysis.

LC Class. No.: QA164 / .K86 2009

Dewey Class. No.: 511/.6

Combinatorics : = the Rota way /
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245 1 0 $a Combinatorics : $b the Rota way / $c Joseph P.S. Kung, Gian-Carlo Rota, Catherine H. Yan.
260 $a Cambridge, UK ; $a New York : $c 2009. $b Cambridge University Press,
300 $a xii, 396 p. : $b ill. ; $c 24 cm.
440 1 $a Cambridge mathematical library
504 $a Includes bibliographical references (p. 369-388) and index.
505 0 0 $t Sets, Functions, and Relations. Sets, valuations, and Boolean algebras -- $t Partially ordered sets -- $t Lattices -- $t Functions, partitions, and entropy -- $t Relations -- $t Matching Theory. What is matching theory? -- $t The marriage theorem -- $t Free and incidence matrices -- $t Submodular functions and independent matchings -- $t Rado's theorem on subrelations -- $t Doubly stochastic matrices -- $t The Gale-Ryser theorem -- $t Matching theory in higher dimensions -- $t Partially Ordered Sets and Lattices. M鋌bius functions -- $t Chains and antichains -- $t Sperner theory -- $t Modular and linear lattices -- $t Finite modular and geometric lattices -- $t Valuation rings and M鋌bius algebras -- $t Generating Functions and the Umbral Calculus. Generating functions -- dt Elementary umbral calculus -- $t Polynomial sequences of binomial type -- $t Sheffer sequences -- $t Umbral composition and connection matrices -- $t The Riemann zeta function -- $t Symmetric Functions and Baxter Algebras. Symmetric functions -- $t Distribution, occupancy, and the partition lattice -- $t Enumeration under a group action -- $t Baxter operators -- $t Free Baxter algebras -- $t Identities in Baxter algebras -- $t Symmetric functions over finite fields -- $t Historical remarks and further reading -- $t Determinants, Matrices, and Polynomials. Polynomials -- $t Apolarity -- $t Grace's theorem -- $t Multiplier sequences -- $t Totally positive matrices -- $t Exterior algebras and compound matrices -- $t Eigenvalues of totally positive matrices -- $t Variation decreasing matrices -- $t Polya frequency sequences -- $t Selected Solutions.
520 8 $a Gian-Carlo Rota was one of the most original and colourful mathematicians of the 20th century. Written by two of his former students, this book is based on notes from his influential graduate courses and on face-to-face discussions.
650 0 $a Combinatorial analysis. $3 523878
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700 1 $a Yan, Catherine H. $3 1041601
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830 0 $a Cambridge mathematical library. $3 1041603