arXiv subjects

Rachelle R. Bouchat

Publications and source records attributed to Rachelle R. Bouchat.

2 recordsLinked to original sources

arXiv2017

Minimal Free Resolutions of $2\times n$ Domino Tilings

We introduce a squarefree monomial ideal associated to the set of domino tilings of a $2\times n$ rectangle and proceed to study the associated minimal free resolution. In this paper, we use results of Dalili and Kummini to show that the Betti numbers of the ideal are independent of the underlying characteristic of the field, and apply a natural splitting to explicitly determine the projective dimension and Castelnuovo-Mumford regularity of the ideal.

math.AC↗

arXiv2011

Path ideals of rooted trees and their graded Betti numbers

Let $Γ$ be a rooted tree and let $t$ be a positive integer. We study algebraic invariants and properties of the path ideal generated by monomial corresponding to paths of length $(t-1)$ in $Γ$. In particular, we give a recursive formula to compute the graded Betti numbers, a general bound for the regularity, an explicit computation of the linear strand, and we characterize when this path ideal has a linear resolution.

math.AC↗