Counting with symmetric functions

DOI10.1007/978-3-319-23618-6zbMath1409.05004OpenAlexW4298857404MaRDI QIDQ495643

Anthony Mendes, Jeffery B. Remmel

Publication date: 14 September 2015

Published in: Developments in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-23618-6

zbMATH Keywords

generating functionssymmetric functionspermutation statisticsPólya's enumeration theoremRobinson-Schensted-Knuth algorithm

Mathematics Subject Classification ID

Research exposition (monographs, survey articles) pertaining to combinatorics (05-02) Exact enumeration problems, generating functions (05A15) Combinatorial identities, bijective combinatorics (05A19) Permutations, words, matrices (05A05) Symmetric functions and generalizations (05E05) Other special functions (33E99) Group actions on combinatorial structures (05E18)

Related Items

Quasisymmetric and Schur expansions of cycle index polynomials, The Pelletier--Ressayre hidden symmetry for Littlewood--Richardson coefficients, The combinatorics of Jeff Remmel, Generalized matrix polynomials of tree Laplacians indexed by symmetric functions and the GTS poset, Chebyshev's bias for products of \(k\) primes, Consecutive up-down patterns in up-down permutations, Symmetric functions and a natural framework for combinatorial and number theoretic sequences, The first infinite family of orthogonal Steiner systems \(\mathrm{S}(3,5,v)\), A combinatorial formula for the Schur coefficients of chromatic symmetric functions, Kronecker powers of harmonics, polynomial rings, and generalized principal evaluations, The \(e\)-positivity of two classes of cycle-chord graphs, Unnamed Item, Chebyshev's bias for products of irreducible polynomials, Gamma-positivity in combinatorics and geometry, Abacus proofs of Cauchy product identities for Schur polynomials, Unnamed Item, A proof of the Murnaghan-Nakayama rule using Specht modules and tableau combinatorics, Position sequences and a \(q\)-analogue for the modular hook length formula, Petrie symmetric functions, The \(e\)-positivity and Schur positivity of some spiders and broom trees