Zobrazeno 1 - 10
of 43
pro vyhledávání: '"13F55, 05E45"'
We find identities involving differential operators in the generic artinian reduction of the Stanley-Reisner ring of a simplicial sphere in any positive characteristic. These identities generalize the characteristic 2 identities used by Papadakis and
Externí odkaz:
http://arxiv.org/abs/2412.04561
We introduce the notion of power lattices that unifies and extends the equicardinal geometric lattices, Cartesian products of subspace lattices, and multiset subset lattices, among several others. The notions of shellability for simplicial complexes,
Externí odkaz:
http://arxiv.org/abs/2407.08629
Autor:
Holleben, Thiago
The theory of Rees algebras of monomial ideals has been extensively studied, and as a consequence, many (sometimes partial) equivalences between algebraic properties of monomial ideals, and combinatorial properties of simplicial complexes and hypergr
Externí odkaz:
http://arxiv.org/abs/2404.12471
Autor:
Patra, Sourav Kanti, Roy, Amit
Let $G$ be a finite simple graph on the vertex set $V(G)$ and let $r$ be a positive integer. We consider the hypergraph $\mathrm{Con}_r(G)$ whose vertices are the vertices of $G$ and the (hyper)edges are all $A\subseteq V(G)$ such that $|A|=r+1$ and
Externí odkaz:
http://arxiv.org/abs/2311.07308
A celebrated theorem of Fr\"oberg gives a complete combinatorial classification of quadratic square-free monomial ideals with a linear resolution. A generalization of this theorem to higher degree square-free monomial ideals is an active area of rese
Externí odkaz:
http://arxiv.org/abs/2311.02430
Autor:
Koolani, Mozhgan, Mafi, Amir
Publikováno v:
Transactions on Combinatorics 2024
Let $R=K[x_1,\ldots,x_n]$ be the polynomial ring in $n$ variables over a field $K$. We show that if $G$ is a connected graph with a basic $5$-cycle $C$, then $G$ is a sequentially Cohen-Macaulay graph if and only if there exists a shedding vertex $x$
Externí odkaz:
http://arxiv.org/abs/2308.04979
A conjecture of Kalai asserts that for $d\geq 4$, the affine type of a prime simplicial $d$-polytope $P$ can be reconstructed from the space of affine $2$-stresses of $P$. We prove this conjecture for all $d\geq 5$. We also prove the following genera
Externí odkaz:
http://arxiv.org/abs/2306.09816
We consider Artinian level algebras arising from the whiskering of a graph. Employing a result by Dao-Nair we show that multiplication by a general linear form has maximal rank in degrees 1 and $n-1$ when the characteristic is not two, where $n$ is t
Externí odkaz:
http://arxiv.org/abs/2306.04393
We prove the local motivic monodromy conjecture for singularities that are nondegenerate with respect to a simplicial Newton polyhedron. It follows that all poles of the local topological zeta functions of such singularities correspond to eigenvalues
Externí odkaz:
http://arxiv.org/abs/2209.03553
Given an arbitrary hypergraph $\mathcal{H}$, we may glue to $\mathcal{H}$ a family of hypergraphs to get a new hypergraph $\mathcal{H}'$ having $\mathcal{H}$ as an induced subhypergraph. In this paper, we introduce three gluing techniques for which t
Externí odkaz:
http://arxiv.org/abs/2110.12170