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|a QA164
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|a Kung, Joseph P. S.
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|a Combinatorics :
|b the Rota way /
|c Joseph P.S. Kung, Gian-Carlo Rota, Catherine H. Yan.
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| 260 |
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|a Cambridge, UK ;
|a New York :
|b Cambridge University Press,
|c 2009.
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| 300 |
|
|
|a xii, 396 p. :
|b ill. ;
|c 23 cm.
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| 490 |
1 |
|
|a Cambridge mathematical library
|
| 504 |
|
|
|a Includes bibliographical references (p. 369-388) and index.
|
| 505 |
0 |
|
|a Sets, Functions, and Relations. Sets, valuations, and Boolean algebras -- Partially ordered sets -- Lattices -- Functions, partitions, and entropy -- Relations -- Matching Theory. What is matching theory? -- The marriage theorem -- Free and incidence matrices -- Submodular functions and independent matchings -- Rado's theorem on subrelations -- Doubly stochastic matrices -- The Gale-Ryser theorem -- Matching theory in higher dimensions -- Partially Ordered Sets and Lattices. Möbius functions -- Chains and antichains -- Sperner theory -- Modular and linear lattices -- Finite modular and geometric lattices -- Valuation rings and Möbius algebras -- Generating Functions and the Umbral Calculus. Generating functions -- Elementary umbral calculus -- Polynomial sequences of binomial type -- Sheffer sequences -- Umbral composition and connection matrices -- The Riemann zeta function -- Symmetric Functions and Baxter Algebras. Symmetric functions -- Distribution, occupancy, and the partition lattice -- Enumeration under a group action -- Baxter operators -- Free Baxter algebras -- Identities in Baxter algebras -- Symmetric functions over finite fields -- Historical remarks and further reading -- Determinants, Matrices, and Polynomials. Polynomials -- Apolarity -- Grace's theorem -- Multiplier sequences -- Totally positive matrices -- Exterior algebras and compound matrices -- Eigenvalues of totally positive matrices -- Variation decreasing matrices -- Pólya frequency sequences -- Selected Solutions.
|
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|a Rota, Gian-Carlo,
|d 1932-1999.
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|a Combinatorial analysis.
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|a Rota, Gian-Carlo,
|d 1932-1999.
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|a Yan, Catherine H.
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|a Cambridge mathematical library.
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