相关论文: Equivalences on Acyclic Orientations

We study the hairy graph homology of a cyclic operad; in particular we show how to assemble corresponding hairy graph cohomology classes to form cocycles for ordinary graph homology, as defined by Kontsevich. We identify the part of hairy…

Let $G$ be a finite graph and $\kappa(G)$ the vertex connectivity of $G$. A chordal graph $G$ is called chordal$^*$ if no vertex of $G$ is adjacent to all other vertices of $G$. Using the syzygy theory in commutative algebra, it is proved…

Let $G$ be a finite group and let $S$ be an inverse-closed subset of $G$ not containing the identity. The Cayley graph $\mathrm{Cay}(G,S)$ has vertex set $G$, where two vertices $x$ and $y$ are adjacent if and only if $x^{-1}y \in S$.…

The problem of classifying equivalence classes of presentations up to isomorphism of Cayley graphs is considered in this article in the case of dicyclic groups. The number of equivalence classes of presentations is uniformly bounded - it is…

We generalize a recent construction of Exel and Pardo, from discrete groups acting on finite directed graphs to locally compact groups acting on topological graphs. To each cocycle for such an action, we construct a $C^*$-correspondence…

In this thesis, we study the combinatorics of cyclically fully commutative elements in Coxeter groups of type $A$ as it relates to conjugacy. In particular, we introduce the notion of cylindrical heaps and ring equivalence in order to state…

We study topological quivers $Q$ admitting a free and proper action by a locally compact group $G$ together with their associated $C^*$-algebras. On the topological side, we provide a complete classification of topological quivers which…

Let U be a unipotent group over the field of complex numbers C, acting on a complex algebraic variety X. Assume that there exists a surjective morphism of complex algebraic varieties f: X --> Y whose fibres are orbits of U. We show that if…

This paper deals with the extension of partial actions of topological groups on topological spaces. Within this framework, we introduce a class of topological embeddings defined via the inverse semigroup of homeomorphisms between open…

The \textit{boxicity} (\textit{cubicity}) of an undirected graph $\Gamma$ is the smallest non-negative integer $k$ such that $\Gamma$ can be represented as the intersection graph of axis-parallel rectangular boxes (unit cubes) in…

The symmetric edge polytope ($\mathrm{SEP}$) of a finite simple graph $G$ is a centrally symmetric lattice polytope whose vertices are defined by the edges of the graph. Among the information encoded by these polytopes are the symmetries of…

Topological quivers generalize the notion of directed graphs in which the sets of vertices and edges are locally compact (second countable) Hausdorff spaces. Associated to a topological quiver $Q$ is a $C^*$-correspondence, and in turn, a…

We prove two results on convex subsets of Euclidean spaces invariant under an orthogonal group action. First, we show that invariant spectrahedra admit an equivariant spectrahedral description, i.e., can be described by an equivariant…

We demonstrate that when a graph exhibits a specific type of symmetry, it satisfies the Union Closed Conjecture(UCC). Additionally, we show that certain graph classes, such as Cylindrical Grid Graphs and Torus Grid Graphs also satisfy the…

A mixed dihedral group is a group $H$ with two disjoint subgroups $X$ and $Y$, each elementary abelian of order $2^n$, such that $H$ is generated by $X\cup Y$, and $H/H'\cong X\times Y$. In this paper, for each $n\geq 2$, we construct a…

For a group $G,$ the generating graph of $G,$ denoted by $\Gamma(G).$ We define $Q_n=\langle x,y: x^{2n}=y^4=1, x^n=y^2,y^{-1}xy=x^{-1}\rangle,$ the dicyclic group of order $4n.$ This paper primarily delves into exploring the graph…

Let P and Q be convex polyhedra in E3 with face lattices F(P) and F(Q) and symmetry groups G(P) and G(Q), respectively. Then, P and Q are called face equivalent if there is a lattice isomorphism between F(P) and F(Q); P and Q are called…

In this paper we introduce an inverse semigroup $\mathcal{S}(E,C)$ associated to a separated graph $(E,C)$ and describe its internal structure. In particular we show that it is strongly $E^*$-unitary and can be realized as a partial…

Using equivariant obstruction theory we construct equivariant maps from certain classifying spaces to representation spheres for cyclic groups, product of elementary Abelian groups and dihedral groups. Restricting them to finite skeleta…

Let k be an algebraically closed field of characteristic p>>0. Let $X\rightarrow Y$ be a symplectic resolution. There are two questions which motivates this work. One question is a construction of an action of a group on the category…