Gamma-positivity in combinatorics and geometry
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Publication:1993954
zbMath1440.05195arXiv1711.05983MaRDI QIDQ1993954
Publication date: 6 November 2018
Published in: Séminaire Lotharingien de Combinatoire (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1711.05983
\(h\)-polynomialunimodalityquasisymmetric functionEulerian polynomialflag triangulationgamma-positivitylocal \(h\)-polynomial
Exact enumeration problems, generating functions (05A15) Bernoulli and Euler numbers and polynomials (11B68) Permutations, words, matrices (05A05) Symmetric functions and generalizations (05E05) Reflection and Coxeter groups (group-theoretic aspects) (20F55)
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Cites Work
- Generalized noncrossing partitions and combinatorics of Coxeter groups
- Fonctions symétriques et séries hypergéométriques basiques multivariées
- THE GEOMETRY OF TORIC VARIETIES
- Subdivisions and Local h-Vectors
- The Upper Bound Conjecture and Cohen-Macaulay Rings
- Counterexamples to the Neggers-Stanley conjecture
- The local $h$-polynomial of the edgewise subdivision of the simplex
- Eulerian Numbers
- A Combinatorial Analogue of Poincaré's Duality Theorem
- On the Shard Intersection Order of a Coxeter Group
- The cd-index of fans and posets
- The 𝐬-Eulerian polynomials have only real roots
- Toric Topology
- Ordered structures and partitions
- Enriched 𝑃-Partitions
- Combinatorial algebraic topology
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Chromatic quasisymmetric functions
- Proof of Gessel's \(\gamma\)-positivity conjecture
- On \(\gamma\)-positive polynomials arising in pattern avoidance
- Excedances in classical and affine Weyl groups
- Counting Dyck paths by area and rank
- A group action on derangements
- The \(\gamma\)-positivity of basic Eulerian polynomials via group actions
- Counting with symmetric functions
- On 1212-avoiding restricted growth functions
- The decrease value theorem with an application to permutation statistics
- Eulerian quasisymmetric functions
- Counting derangements, involutions and unimodal elements in the wreath product \(C_r\wr\mathfrak S_n\)
- Equivariant Ehrhart theory
- On \(\gamma \)-vectors satisfying the Kruskal-Katona inequalities
- The symmetric and unimodal expansion of Eulerian polynomials via continued fractions
- Flag subdivisions and \(\gamma\)-vectors
- The local \(h\)-vector of the cluster subdivision of a simplex
- Some combinatorial and algebraic properties of Coxeter complexes and Tits buildings
- Matroid polytopes, nested sets and Bergman fans
- On the excedance number of colored permutation groups
- Nested complexes and their polyhedral realizations
- Enriched \(P\)-partitions and peak algebras
- Local \(h\)-polynomials, invariants of subdivisions, and mixed Ehrhart theory
- Symmetric unimodal expansions of excedances in colored permutations
- \(f\)-vectors of barycentric subdivisions
- On certain combinatorial expansions of the Eulerian polynomials
- Rational points and Coxeter group actions on the cohomology of toric varieties
- Faces of generalized permutohedra
- Triangulations. Structures for algorithms and applications
- A symmetrical Eulerian identity
- Affine descents and the Steinberg torus
- The Veronese construction for formal power series and graded algebras
- On derangement polynomials of type \(B\). II
- Remarks on missing faces and generalized lower bounds on face numbers
- Bijections for Cayley trees, spanning trees, and their q-analogues
- The number of faces of a simplicial convex polytope
- Some aspects of groups acting on finite posets
- On the structure of the lattice of noncrossing partitions
- Eulerian numbers, tableaux, and the Betti numbers of a toric variety
- Cohen-Macaulay quotients of polynomial rings
- On the Neggers-Stanley conjecture and the Eulerian polynomials
- Permutation statistics of indexed permutations
- Counting permutations with given cycle structure and descent set
- Some permutation representations of Weyl groups associated with the cohomology of toric varieties
- A character formula for the representation of a Weyl group in the cohomology of the associated toric variety
- \(q\)-Eulerian polynomials arising from Coxeter groups
- Flag \(f\)-vectors and the \(cd\)-index
- Intransitive trees
- Cycle type and descent set in wreath products
- Vanishing theorems and conjectures for the 2-homology of right-angled Coxeter groups
- \(Y\)-systems and generalized associahedra
- Local \(h\)-vectors of quasi-geometric and barycentric subdivisions
- Schur positivity and labeled binary trees
- Coxeter-bicatalan combinatorics
- On the Charney-Davis and Neggers-Stanley conjectures
- Sign-graded posets, unimodality of {\(W\)}-polynomials and the {C}harney-{D}avis conjecture
- Segre and Rees products of posets, with ring-theoretic applications
- \(K(\pi,1)\)'s for Artin groups of finite type.
- Chow rings of toric varieties defined by atomic lattices
- Combinatorics and commutative algebra.
- The Euler characteristic of a nonpositively curved, piecewise Euclidean manifold
- Counting forests by descents and leaves
- Frankl-Füredi-Kalai inequalities on the \(\gamma\)-vectors of flag nestohedra
- Rearrangements of the symmetric group and enumerative properties of the tangent and secant numbers
- A note on the number of \(k\)-roots in \(S_{n}\)
- Character formulas and descents for the hyperoctahedral group
- Two new triangles of \(q\)-integers via \(q\)-Eulerian polynomials of type \(A\) and \(B\)
- Derangement polynomials and excedances of type \(B\)
- Poset homology of Rees products, and \(q\)-Eulerian polynomials
- Symmetric decompositions and the strong Sperner property for noncrossing partition lattices
- Some combinatorial properties of flag simplicial pseudomanifolds and spheres
- The \(\gamma \)-vector of a barycentric subdivision
- Rees products and lexicographic shellability
- Decomposition theorem for the cd-index of Gorenstein posets
- Actions on permutations and unimodality of descent polynomials
- Coxeter cones and their \(h\)-vectors
- Colored-descent representations of complex reflection groups \(G(r,p,n)\).
- Subdivisions of toric complexes
- The Eulerian distribution on involutions is indeed unimodal
- The descent statistic on involutions is not log-concave
- Théorie géométrique des polynômes eulériens
- A proof of the lower bound conjecture for convex polytopes
- Real root conjecture fails for five- and higher-dimensional spheres
- A note on the \(\gamma\)-coefficients of the tree Eulerian polynomial
- Two-Sided Eulerian Numbers via Balls in Boxes
- Edgewise Subdivisions, Local $h$-Polynomials, and Excedances in the Wreath Product $\mathbb{Z}_r \wr \mathfrak{S}_n$
- Unimodality, log-concavity, real-rootedness and beyond
- A survey of subdivisions and local $h$-vectors
- The contributions of Stanley to the fabric of symmetric and quasisymmetric functions
- From Poset Topology to $q$-Eulerian Polynomials to Stanley's Chromatic Symmetric Functions
- Proof of Gal's conjecture for theDseries of generalized associahedra
- Combinatorics of Coxeter Groups
- Runs, Slides and Moments
- The dual braid monoid
- Counterexamples to the poset conjectures of Neggers, Stanley, and Stembridge
- The combinatorics of twisted involutions in Coxeter groups
- Unimodal, log-concave and Pólya frequency sequences in combinatorics
- Unimodal Polynomials Arising from Symmetric Functions
- Cubical realizations of flag nestohedra and proof of Gal's conjecture for them
- Permutohedra, Associahedra, and Beyond