Related papers: Composition of simplicial complexes, polytopes and…
We investigate the relationship between the complex symmetry of composition operators $C_{\phi}f=f\circ \phi$ induced on the classical Hardy space $H^2(\mathbb{D})$ by an analytic self-map $\phi$ of the open unit disk $\mathbb{D}$ and its…
A simplicial complement P is a sequence of subsets of [m] and the simplicial complement P corresponds to a unique simplicial complex K with vertices in [m]. In this paper, we defined the homology of a simplicial complement…
When G is a region in the complex plane, compact composition operators on the uniform algebra of bounded analytic functions on G and the spectra of these operators were described by D. Swanton, Compact composition operators on B(D), Proc.…
In this paper, we use subword complexes to provide a uniform approach to finite type cluster complexes and multi-associahedra. We introduce, for any finite Coxeter group and any nonnegative integer k, a spherical subword complex called…
Let $\Delta$ be simplicial complex and let $k[\Delta]$ denote the Stanley--Reisner ring corresponding to $\Delta$. Suppose that $k[\Delta]$ has a pure free resolution. Then we describe the Betti numbers and the Hilbert--Samuel multiplicity…
This paper is concerned with spherical harmonics, and two refinements thereof: complex harmonics and symplectic harmonics. The reproducing kernels of the spherical and complex harmonics are explicitly given in terms of Gegenbauer or Jacobi…
In this paper, we introduce higher symmetric simplicial complexity $SC_n^{\Sigma}(K)$ of a simplicial complex $K$ and higher symmetric combinatorial complexity $CC_n^{\Sigma}(P)$ of a finite poset $P$. These are simplicial and combinatorial…
A new formula is obtained in algebraic topology, in terms of Betti numbers, and a new method, called the spinal method, is suggested and developed for generating quadrangulations of closed orientable surfaces. Those surfaces arise as the…
Generalizing the decomposition of a connected planar graph into a tree and a dual tree, we prove a combinatorial analog of the classic Helmholz-Hodge decomposition of a smooth vector field. Specifically, we show that for every polyhedral…
Skeletal polyhedra and polygonal complexes are finite or infinite periodic structures in 3-space with interesting geometric, combinatorial, and algebraic properties. These structures can be viewed as finite or infinite periodic graphs…
A classical combinatorial fact is that the simplicial complex consisting of disjointly embedded chords in a convex planar polygon is a sphere. For any surface F with non-empty boundary, there is an analogous complex Arc(F) consisting of…
A few years ago Kramer and Laubenbacher introduced a discrete notion of homotopy for simplicial complexes. In this paper, we compute the discrete fundamental group of the order complex of the Boolean lattice. As it turns out, it is…
This paper provides a class of complex symmetric weighted composition operators on $H^2(\mathbb{D})$ to includes the unitary subclass, the Hermitian subclass and the normal subclass obtained by Bourdon and Noor. A characterization of…
The partition number $\pi(K)$ of a simplicial complex $K\subset 2^{[m]}$ is the minimum integer $\nu$ such that for each partition $A_1\uplus\ldots\uplus A_\nu = [m]$ of $[m]$ at least one of the sets $A_i$ is in $K$. A complex $K$ is…
This paper makes some preliminary observations towards an extension of current work on graphs defined on groups to simplicial complexes. I define a variety of simplicial complexes on a group which are preserved by automorphisms of the…
Simplicial complexes are a popular tool used to model higher-order interactions between elements of complex social and biological systems. In this paper, we study some combinatorial aspects of a class of simplicial complexes created by a…
In this paper, a quantum computational framework for algebraic topology based on simplicial set theory is presented. This extends previous work, which was limited to simplicial complexes and aimed mostly to topological data analysis. The…
We determine, in an inductive framework, the vertices of the polytope $P(s,K)$ controlling the conjugacy classes of elements which product to one in the maximal compact subgroup $K$ of a simple complex algebraic group $G$. This extends…
A fixed knot $K$ acts via Murasugi sum on the space $\mathcal{S}$ of isotopy classes of knots. This operation endows $\mathcal{S}$ with a directed graph structure denoted by $M\kern-1pt SG(K)$. We show that any given family of knots in…
It is known that there are finitely many simplicial complexes (up to isomorphism) with a given number of vertices. Translating to the language of $h$-vectors, there are finitely many simplicial complexes of bounded dimension with $h_1=k$…