Zobrazeno 1 - 10
of 151
pro vyhledávání: '"Kubitzke, Martina"'
We generalize the definition of the $cd$-index of an Eulerian poset to the class of semi-Eulerian posets. For simplicial semi-Eulerian Buchsbaum posets, we show that all coefficients of the $cd$-index are non-negative. This proves a conjecture of Nov
Externí odkaz:
http://arxiv.org/abs/2405.05812
The study of the Lefschetz properties of Artinian graded algebras was motivated by the hard Lefschetz theorem for a smooth complex projective variety, a breakthrough in algebraic topology and geometry. Over the last few years, this topic has attracte
Externí odkaz:
http://arxiv.org/abs/2311.03081
We study signals that are sparse in graph spectral domain and develop explicit algorithms to reconstruct the support set as well as partial components from samples on few vertices of the graph. The number of required samples is independent of the tot
Externí odkaz:
http://arxiv.org/abs/2310.11292
Starting from any finite simple graph, one can build a reflexive polytope known as a symmetric edge polytope. The first goal of this paper is to show that symmetric edge polytopes are intrinsically matroidal objects: more precisely, we prove that two
Externí odkaz:
http://arxiv.org/abs/2307.04933
A cosmological polytope is defined for a given Feynman diagram, and its canonical form may be used to compute the contribution of the Feynman diagram to the wavefunction of certain cosmological models. Given a subdivision of a polytope, its canonical
Externí odkaz:
http://arxiv.org/abs/2303.05876
Given a (finite) simplicial complex, we define its $i$-th Laplacian polytope as the convex hull of the columns of its $i$-th Laplacian matrix. This extends Laplacian simplices of finite simple graphs, as introduced by Braun and Meyer. After studying
Externí odkaz:
http://arxiv.org/abs/2301.11602
Given an ascending chain $(I_n)_{n\in\mathbb{N}}$ of $\Sym$-invariant squarefree monomial ideals, we study the corresponding chain of Alexander duals $(I_n^\vee)_{n\in\mathbb{N}}$. Using a novel combinatorial tool, which we call \emph{avoidance up to
Externí odkaz:
http://arxiv.org/abs/2209.14132
Publikováno v:
SIAM Journal on Discrete Mathematics 37 (2023), no. 2, pp. 487-515
We study $\gamma$-vectors associated with $h^*$-vectors of symmetric edge polytopes both from a deterministic and a probabilistic point of view. On the deterministic side, we prove nonnegativity of $\gamma_2$ for any graph and completely characterize
Externí odkaz:
http://arxiv.org/abs/2201.09835
Given a graph $G=(V,E)$ and a set $S \subseteq \binom{V}{2}$ of terminal pairs, the minimum multicut problem asks for a minimum edge set $\delta \subseteq E$ such that there is no $s$-$t$-path in $G -\delta$ for any $\{s,t\}\in S$. For $|S|=1$ this i
Externí odkaz:
http://arxiv.org/abs/2112.01095
Horizontal visibility graphs (HVGs, for short) are a common tool used in the analysis and classification of time series with applications in many scientific fields. In this article, extending previous work by Lacasa and Luque, we prove that HVGs asso
Externí odkaz:
http://arxiv.org/abs/2111.02723