On the Neggers-Stanley conjecture and the Eulerian polynomials

DOI10.1006/jcta.1997.2839zbMath0911.05005OpenAlexW2074351421WikidataQ123021612 ScholiaQ123021612MaRDI QIDQ1268618

Vesselin N. Gasharov

Publication date: 4 May 1999

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jcta.1997.2839

zbMATH Keywords

labelingpermutationunimodallog-concaveNeggers-Stanley conjecture

Mathematics Subject Classification ID

Combinatorics of partially ordered sets (06A07) Algebraic combinatorics (05E99) Enumerative combinatorics (05A99)

Related Items (17)

Lattice paths and \((n - 2)\)-stack sortable permutations ⋮ The Eulerian distribution on the fixed-point free involutions of the hyperoctahedral group ⋮ On certain combinatorial expansions of the Eulerian polynomials ⋮ A context-free grammar for the \(e\)-positivity of the trivariate second-order Eulerian polynomials ⋮ Actions on permutations and unimodality of descent polynomials ⋮ Coxeter cones and their \(h\)-vectors ⋮ Gamma-positivity in combinatorics and geometry ⋮ On the Charney-Davis and Neggers-Stanley conjectures ⋮ Preservation of log-concavity on summation ⋮ Linear extensions of ranked posets, enumerated by descents. A problem of Stanley from the 1981 Banff conference on ordered sets ⋮ The Eulerian distribution on involutions is indeed unimodal ⋮ The Eulerian distribution on the involutions of the hyperoctahedral group is indeed \(\gamma \)-positive ⋮ Tree descent polynomials: unimodality and central limit theorem ⋮ Enumerating \(S_n\) by associated transpositions and linear extensions of finite posets ⋮ A combinatorial proof of the log-concavity of the numbers of permutations with \(k\) runs ⋮ Counterexamples to the poset conjectures of Neggers, Stanley, and Stembridge ⋮ A simplicial complex of 2-stack sortable permutations

Cites Work

• A multiindexed Sturm sequence of polynomials and unimodality of certain combinatorial sequences
• Binomial determinants, paths, and hook length formulae
• Eulerian numbers, tableaux, and the Betti numbers of a toric variety
• Enumeration of functions from posets to chains
• \(h\)-shellings and \(h\)-complexes
• Hilbert polynomials in combinatorics
• Combinatorics and total positivity
• On the generating functions of totally positive sequences. I
• Unimodal, log-concave and Pólya frequency sequences in combinatorics
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