Zobrazeno 1 - 10
of 276
pro vyhledávání: '"Van Tuyl, Adam"'
Let $\Delta$ be a pure simplicial complex on $n$ vertices having dimension $d$ and codimension $c = n-d-1$ in the simplex. Terai and Yoshida proved that if the number of facets of $\Delta$ is at least $\binom{n}{c}-2c+1$, then $\Delta$ is Cohen-Macau
Externí odkaz:
http://arxiv.org/abs/2403.07316
We study three invariants of geometrically vertex decomposable ideals: the Castelnuovo-Mumford regularity, the multiplicity, and the $a$-invariant. We show that these invariants can be computed recursively using the ideals that appear in the geometri
Externí odkaz:
http://arxiv.org/abs/2311.08541
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
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
Autor:
Biermann, Jennifer, Castellano, Beth Anne, Manivel, Marcella, Petrucelli, Eden, Van Tuyl, Adam
We introduce a family of graphs, which we call down-left graphs, and study their combinatorial and algebraic properties. We show that members of this family are well-covered, $C_5$-free, and vertex decomposable. By applying a result of H\`a-Woodroofe
Externí odkaz:
http://arxiv.org/abs/2304.14528
Autor:
Bhaskara, Kieran, Van Tuyl, Adam
Publikováno v:
Proc. Amer. Math. Soc. Ser. B 10 (2023), 219-232
Let $G$ be a finite simple graph and let $I_G$ denote its associated toric ideal in the polynomial ring $R$. For each integer $n\geq 2$, we completely determine all the possible values for the tuple $({\rm reg}(R/I_G), {\rm deg}(h_{R/I_G}(t)),{\rm pd
Externí odkaz:
http://arxiv.org/abs/2303.14818
The Fiedler matrices are a large class of companion matrices that include the well-known Frobenius companion matrix. The Fiedler matrices are part of a larger class of companion matrices that can be characterized with a Hessenberg form. In this paper
Externí odkaz:
http://arxiv.org/abs/2301.13257
Autor:
Atar, Büşra, Bhaskara, Kieran, Cook, Adrian, Da Silva, Sergio, Harada, Megumi, Rajchgot, Jenna, Van Tuyl, Adam, Wang, Runyue, Yang, Jay
We study the Hadamard product of two varieties $V$ and $W$, with particular attention to the situation when one or both of $V$ and $W$ is a binomial variety. The main result of this paper shows that when $V$ and $W$ are both binomial varieties, and t
Externí odkaz:
http://arxiv.org/abs/2211.14210
Autor:
Cummings, Mike, Van Tuyl, Adam
Publikováno v:
J. Softw. Alg. Geom. 14 (2024) 41-50
Using the geometric vertex decomposition property first defined by Knutson, Miller, and Yong, a recursive definition for geometrically vertex decomposable ideals was given by Klein and Rajchgot. We introduce the Macaulay2 package GeometricDecomposabi
Externí odkaz:
http://arxiv.org/abs/2211.02471
Publikováno v:
Algebraic Combinatorics, Vol. 6 (2023), No. 4, p. 965-997
The geometric vertex decomposability property for polynomial ideals is an ideal-theoretic generalization of the vertex decomposability property for simplicial complexes. Indeed, a homogeneous geometrically vertex decomposable ideal is radical and Coh
Externí odkaz:
http://arxiv.org/abs/2207.06391