Combinatorics : the Rota way

Combinatorics : the Rota way / Joseph P.S. Kung, Gian-Carlo Rota, Catherine H. Yan.

में बचाया:
ग्रंथसूची विवरण
मुख्य लेखक: Kung, Joseph P. S.
अन्य लेखक: Rota, Gian-Carlo, 1932-1999, Yan, Catherine H.
स्वरूप: पुस्तक
भाषा:English
प्रकाशित: Cambridge, UK ; New York : Cambridge University Press, 2009.
श्रृंखला:Cambridge mathematical library.
विषय:
Rota, Gian-Carlo, > 1932-1999.
Combinatorial analysis.
विषय - सूची:
  • 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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