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pro vyhledávání: '"05E45"'
In this paper, we develop the concept of multiple cylinder of relations which is a generalization of the relation cylinder, extending the multiple non-Hausdorff mapping cylinder to sequences of finite T0-spaces linked by a series of relations. This c
Externí odkaz:
http://arxiv.org/abs/2411.09281
Autor:
Goeckner, Bennet, Pavelka, Marta
Unit interval and interval complexes are higher-dimensional generalizations of unit interval and interval graphs, respectively. We show that strongly connected unit interval complexes are shellable with shellings induced by their unit interval orders
Externí odkaz:
http://arxiv.org/abs/2411.08245
An outerplanar graph is a planar graph that has a planar drawing with all vertices on the unbounded face. The matching complex of a graph is the simplicial complex whose faces are subsets of disjoint edges of the graph. In this paper we prove that th
Externí odkaz:
http://arxiv.org/abs/2411.04601
We study algebraic shifting of uniform hypergraphs and finite simplicial complexes in the exterior algebra with respect to matrices which are not necessarily generic. Several questions raised by Kalai (2002) are addressed. For instance, it turns out
Externí odkaz:
http://arxiv.org/abs/2410.24044
Autor:
Studený, Milan
Five different ways of combinatorial description of non-empty faces of the cone of supermodular functions on the power set of a finite basic set $N$ are introduced. Their identification with faces of the cone of supermodular games allows one to assoc
Externí odkaz:
http://arxiv.org/abs/2410.19454
A biclique in a graph $G$ is a complete bipartite subgraph (not necessarily induced), and the least positive integer $k$ for which the vertex set of $G$ can be partitioned into at most $k$ bicliques is the biclique vertex partition number $bp(G)$ of
Externí odkaz:
http://arxiv.org/abs/2410.15213
Autor:
Gaetz, Christian, Hersh, Patricia
We study the poset topology of lattices arising from orientations of 1-skeleta of directionally simple polytopes, with Bruhat interval polytopes $Q_{e,w}$ as our main example. We show that the order complex $\Delta ((u,v)_w)$ of an interval therein i
Externí odkaz:
http://arxiv.org/abs/2410.08076
Binary geometries have recently been introduced in particle physics in connection with stringy integrals. In this work, we study a class of simple polytopes, called \emph{pellytopes}, whose number of vertices are given by Pell's numbers. We provide a
Externí odkaz:
http://arxiv.org/abs/2410.08002
Autor:
Planken, Tim
While every plane triangulation is colourable with three or four colours, Heawood showed that a plane triangulation is 3-colourable if and only if every vertex has even degree. In $d \geq 3$ dimensions, however, every $k \geq d+1$ may occur as the ch
Externí odkaz:
http://arxiv.org/abs/2409.11762
The degree of a map between orientable manifolds is a crucial concept in topology, providing deep insights into the structure and properties of the manifolds and the corresponding maps. This concept has been thoroughly investigated, particularly in t
Externí odkaz:
http://arxiv.org/abs/2409.00907