Peak quasisymmetric functions and Eulerian enumeration

DOI10.1016/S0001-8708(02)00067-1zbMath1027.05105arXiv0706.3486MaRDI QIDQ1400995

Samuel K. Hsiao, Billera, Louis J., Stephanie Van Willigenburg

Publication date: 17 August 2003

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

Full work available at URL: https://arxiv.org/abs/0706.3486

zbMATH Keywords

Eulerian posetspeak algebra\(g\)-theoremquasisymmetric functionflag \(f\)-vector\textbf{cd}-index

Mathematics Subject Classification ID

Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) (52B05) Symmetric functions and generalizations (05E05) Algebraic aspects of posets (06A11)

Related Items

Random walks on quasisymmetric functions, The peak algebra and the descent algebras of types B and D, Peak algebras, paths in the Bruhat graph and Kazhdan-Lusztig polynomials, Enriched \(P\)-partitions and peak algebras, Multiplicity free Schur, skew Schur, and quasisymmetric Schur functions, Analysis of casino shelf shuffling machines, The peak algebra and the Hecke-Clifford algebras at \(q=0\), On the distribution of surface extrema in several one- and two-dimensional random landscapes, Eulerian quasisymmetric functions, Floodings of metric graphs, Littlewood-Richardson rules for symmetric skew quasisymmetric Schur functions, Quasisymmetric Schur functions, Row-strict quasisymmetric Schur functions, Enriched toric \([\vec{D}\)-partitions], Equidistribution of set-valued statistics on standard Young tableaux and transversals, Skew quasisymmetric Schur functions and noncommutative Schur functions, Further refinements of Wilf-equivalence for patterns of length 4, Weak quasi-symmetric functions, Rota-Baxter algebras and Hopf algebras, Multigraded combinatorial Hopf algebras and refinements of odd and even subalgebras., The \(r\)-signed Birkhoff transform, Coxeter-Knuth graphs and a signed little map for type B reduced words, The Tchebyshev transforms of the first and second kind, Oriented interval greedoids, A lift of Schur's Q-functions to the peak algebra, Linear inequalities for enumerating chains in partially ordered sets, Dual immaculate quasisymmetric functions expand positively into Young quasisymmetric Schur functions, Quasisymmetric functions and Kazhdan-Lusztig polynomials., Enumeration in convex geometries and associated polytopal subdivisions of spheres, The Hopf algebras of signed permutations, of weak quasi-symmetric functions and of Malvenuto-Reutenauer, The peak algebra of the symmetric group revisited., The pinnacle set of a permutation, On weak peak quasisymmetric functions, Toward a polynomial basis of the algebra of peak quasisymmetric functions, Affine and toric hyperplane arrangements, The 𝑐𝑑-index: A survey, Sorting permutations with fixed pinnacle set, Twisted descent algebras and the Solomon-Tits algebra., A signed analog of the Birkhoff transform

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A new basis of polytopes
• Generalized Dehn-Sommerville relations for polytopes, spheres and Eulerian partially ordered sets
• The number of faces of a simplicial convex polytope
• A new index for polytopes
• Coproducts and the cd-index
• Flag \(f\)-vectors and the \(cd\)-index
• Shifted quasi-symmetric functions and the Hopf algebra of peak functions
• Infinitesimal Hopf algebras and the cd-index of polytopes
• The c--2d-index of oriented matroids
• Noncommutative Pieri operators on posets
• Decompositions of partially ordered sets
• Noncommutative symmetric functions
• Flag vectors of Eulerian partially ordered sets
• Generalizations of Eulerian partially ordered sets, flag numbers, and the Möbius function
• Duality between quasi-symmetric functions and the Solomon descent algebra
• On posets and Hopf algebras
• Linear inequalities for flags in graded partially ordered sets
• Monotonicity of the cd-index for polytopes
• A combinatorial description of the spectrum for the Tsetlin library and its generalization to hyperplane arrangements
• Hilbert schemes, polygraphs and the Macdonald positivity conjecture
• Facing up to arrangements: face-count formulas for partitions of space by hyperplanes
• Balanced Cohen-Macaulay Complexes
• The toric ℎ-vectors of partially ordered sets
• Enriched 𝑃-Partitions
• Noncommutative enumeration in graded posets