Combinatorics : the Rota way /

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.

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Kung, Joseph P. S.
Otros Autores: Rota, Gian-Carlo, 1932-1999, Yan, Catherine H.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cambridge, UK ; New York : Cambridge University Press, 2009.
Colección:Cambridge mathematical library.
Temas:
Rota, Gian-Carlo, > 1932-1999.
Combinatorial analysis.
Analyse combinatoire.
MATHEMATICS > Combinatorics.
Kombinatorik
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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
  • dt 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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