The 𝑐𝑑-index: A survey
From MaRDI portal
Publication:4998736
DOI10.1090/conm/764/15355zbMath1468.05001arXiv1901.04939OpenAlexW3152445110MaRDI QIDQ4998736
Publication date: 9 July 2021
Published in: Polytopes and Discrete Geometry (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1901.04939
Partial orders, general (06A06) Research exposition (monographs, survey articles) pertaining to combinatorics (05-02) Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) (52B05) (n)-dimensional polytopes (52B11) Combinatorics of partially ordered sets (06A07) Combinatorial aspects of simplicial complexes (05E45)
Related Items
On the geometry of flag Hilbert-Poincaré series for matroids, Filtrations on combinatorial intersection cohomology and invariants of subdivisions
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Peak algebras, paths in the Bruhat graph and Kazhdan-Lusztig polynomials
- A lattice path interpretation of the diamond product
- Level Eulerian posets.
- On the complete \(\mathbf{cd}\)-index of a Bruhat interval.
- Shortest path poset of Bruhat intervals
- Regular cell complexes in total positivity.
- Squarefree \( P\)-modules and the \({\mathbf {cd}}\)-index
- On the cd-index and \(\gamma \)-vector of S\(^{\ast}\)-shellable CW-spheres
- Euler flag enumeration of Whitney stratified spaces
- A poset view of the major index.
- The complete \(\mathbf{cd}\)-index of Boolean lattices
- Sweeping the cd-index and the toric \(h\)-vector
- A new basis of polytopes
- The complete \(\mathbf{cd}\)-index of dihedral and universal Coxeter groups
- On the non-existence of an \(R\)-labeling
- The Tchebyshev transforms of the first and second kind
- Oriented interval greedoids
- Posets, regular CW complexes and Bruhat order
- Generalized Dehn-Sommerville relations for polytopes, spheres and Eulerian partially ordered sets
- A signed analog of the Birkhoff transform
- Polyspherical complexes
- \(M\)-vector analogue for the \(\mathbf{cd}\)-index
- Local \(h\)-polynomials, invariants of subdivisions, and mixed Ehrhart theory
- Weighted derivations and the cd-index
- The cd-index of the poset of intervals and \(E_{t}\)-construction
- Flag enumerations of matroid base polytopes
- Affine and toric hyperplane arrangements
- Intersection homology of toric varieties and a conjecture of Kalai
- The number of faces of a simplicial convex polytope
- Bruhat order of Coxeter groups and shellability
- A proof of the sufficiency of McMullen's conditions for f-vectors of simplicial convex polytopes
- A new index for polytopes
- Coproducts and the cd-index
- On flag vectors, the dowling lattice, and braid arrangements
- Flag \(f\)-vectors and the \(cd\)-index
- The homology of partitions with an even number of blocks
- The Mayer-Vietoris and IC equations for convex polytopes
- Infinitesimal Hopf algebras and the cd-index of polytopes
- The c--2d-index of oriented matroids
- Peak quasisymmetric functions and Eulerian enumeration
- Non-negative cd-coefficients of Gorenstein* posets.
- Vanishing theorems and conjectures for the 2-homology of right-angled Coxeter groups
- Lower bounds for the \(cd\)-index of odd-dimensional simplicial manifolds
- Flags and shellings of Eulerian cubical posets
- Noncommutative Pieri operators on posets
- \(k\)-Eulerian posets
- Prisms and pyramids of shelling components
- The cd-indices of intervals in the uncrossing partial order on matchings
- Quasisymmetric functions and Kazhdan-Lusztig polynomials.
- Tchebyshev posets
- Inequalities for the h-vectors and flag h-vectors of geometric lattices
- The \(E_t\)-construction for lattices, spheres and polytopes
- The cd-index of Bruhat intervals.
- Lifting inequalities for polytopes
- On the \(cd\)-variation polynomials of André and Simsun permutations
- Flag vectors of Eulerian partially ordered sets
- Homology of Newtonian coalgebras.
- Inequalities for \textbf{cd}-indices of joins and products of polytopes
- Extremal problems for the Möbius function in the face lattice of the \(n\)-octahedron
- Wonderful models of subspace arrangements
- On posets and Hopf algebras
- Hopf algebra of building sets.
- Cutting polytopes and flag \(f\)-vectors
- Monotonicity of the cd-index for polytopes
- On the non-negativity of the complete \(cd\)-index
- Manifold arrangements
- Decomposition theorem for the cd-index of Gorenstein posets
- The r-cubical lattice and a generalization of the cd-index
- Real root conjecture fails for five- and higher-dimensional spheres
- Families of tight inequalities for polytopes
- Signs in the 𝑐𝑑-index of Eulerian partially ordered sets
- Balanced Cohen-Macaulay Complexes
- Andre Permutations, Lexicographic Shellability and the cd-Index of a Convex Polytope
- The toric ℎ-vectors of partially ordered sets
- Lawrence Polytopes
- The short toric polynomial
- The flag $f$-vectors of Gorenstein* order complexes of dimension $3$
- The cd-index of fans and posets
- Enriched 𝑃-Partitions
- Noncommutative enumeration in graded posets