Related papers: Simplicial Complexes of Triangular Ferrers Boards
We extend the construction of moment-angle complexes to simplicial posets by associating a certain T^m-space Z_S to an arbitrary simplicial poset S on m vertices. Face rings Z[S] of simplicial posets generalise those of simplicial…
In this paper, we prove that each injective simplicial map of the arc complex of a compact, connected, orientable surface with nonempty boundary is induced by a homeomorphism of the surface. We deduce, from this result, that the group of…
We construct embeddings of simplicial complexes into a (surface of a) simplicial ball whose triangulation has bounded degrees and low volume. This construction can be used either to efficiently "simplify a complicated space" by realizing it…
We study the space $Q_n$ of all configurations of $n$ ordered points on the circle such that no three points coincide, and in which one of the points (say, the last one) is fixed. We compute its fundamental group for $n<6$ and describe its…
A polygonal complex in euclidean 3-space is a discrete polyhedron-like structure with finite or infinite polygons as faces and finite graphs as vertex-figures, such that a fixed number r of faces surround each edge. It is said to be regular…
Let $\mathcal{P}$ be a frame polyomino, a new kind of non-simple polyomino. In this paper we study the $h$-polynomial of $K[\mathcal{P}]$ in terms of the switching rook polynomial of $\mathcal{P}$ using the shellable simplicial complex…
In this paper we introduce a new model of random simplicial complexes depending on multiple probability parameters. This model includes the well-known Linial - Meshulam random simplicial complexes and random clique complexes as special…
We prove that the simplicial cocommutative coalgebra of singular chains on a connected topological space determines the homotopy type rationally and one prime at a time, without imposing any restriction on the fundamental group. In…
The Leray number of an abstract simplicial complex is the minimal integer $d$ where its induced subcomplexes have trivial homology groups in dimension $d$ or greater. We give an upper bound on the Leray number of a complex in terms of how…
Crossed complexes are shown to have an algebra sufficiently rich to model the geometric inductive definition of simplices, and so to give a purely algebraic proof of the Homotopy Addition Lemma (HAL) for the boundary of a simplex. This…
We introduce a class of combinatorial singularities of Lagrangian skeleta of symplectic manifolds. The link of each singularity is a finite regular cell complex homotopy equivalent to a bouquet of spheres. It is determined by its face poset…
In this paper, we give a new and efficient algebraic criterion for the pure as well as non-pure shellability of simplicial complex $\Delta$ over [n]. We also give an algebraic characterization of a leaf in a simplicial complex (defined in…
We study the following generalization of Roth's theorem for 3-term arithmetic progressions. For s>1, define a nontrivial s-configuration to be a set of s(s+1)/2 integers consisting of s distinct integers x_1,...,x_s as well as all the…
We consider compact K\"ahlerian manifolds $X$ of even dimension 4 or more, endowed with a log-symplectic structure $\Phi$, a generically nondegenerate closed 2-form with simple poles on a divisor $D$ with local normal crossings. A simple…
This paper is about counting the number of distinct (scattered) subwords occurring in a given word. More precisely, we consider the generalization of the Pascal triangle to binomial coefficients of words and the sequence $(S(n))_{n\ge 0}$…
Much research has been done on structures equivalent to topological or simplicial groups. In this paper, we consider instead simplicial monoids. In particular, we show that the usual model category structure on the category of simplicial…
The theory of shellable simplicial complexes brings together combinatorics, algebra, and topology in a remarkable way. Initially introduced by Alder for $q$-simplicial complexes, recent work of Ghorpade, Pratihar, and Randrianarisoa extends…
In this paper we study the resolution of a facet ideal associated with a special class of simplicial complexes introduced by S. Faridi. These simplicial complexes are called trees, and are a generalization (to higher dimensions) of the…
In 1983 Kalai proved an incredible generalisation of Cayley's formula for the number of trees on a labelled vertex set to a formula for a class of $r$-dimensional simplicial complexes. These simplicial complexes generalise trees by means of…
We attach Hecke polynomials $P_n(F;x)$ to weak Hecke eigenforms $F$ of weight $2-k$ and show that, for large $n$, every zero is simple and lies in $[0,1728]$. The construction pulls back a weakly holomorphic Hecke combination of $F$ along…