8 citations · 22 across the 17 of their papers we have counts for
20 papers
Computing generalized Frobenius powers of monomial ideals
Christopher A. Francisco, Matthew Mastroeni, Jeffrey Mermin +1
Generalized Frobenius powers of an ideal were introduced in work of Hernández, Teixeira, and Witt as characteristic-dependent analogs of test ideals. However, little is known about…
Asymptotic resurgence via integral closures
Michael DiPasquale, Christopher A. Francisco, Jeffrey Mermin +1
Given an ideal in a polynomial ring, we show that the asymptotic resurgence studied by Guardo, Harbourne, and Van Tuyl can be computed using integral closures. As a consequence, th…
The Rees algebra of a two-Borel ideal is Koszul
Michael DiPasquale, Christopher A. Francisco, Jeffrey Mermin +2
Let and be two monomials of the same degree, and let be the smallest Borel ideal containing and . We show that the toric ring of is Koszul by constructing a…
Free and Non-free Multiplicities on the Arrangement
Michael DiPasquale, Christopher A. Francisco, Jeffrey Mermin +1
We give a complete classification of free and non-free multiplicities on the braid arrangement. Namely, we show that all free multiplicities on fall into two families t…
Powers of squarefree monomial ideals and combinatorics
Christopher A. Francisco, Huy Tai Ha, Jeffrey Mermin
We survey research relating algebraic properties of powers of squarefree monomial ideals to combinatorial structures. In particular, we describe how to detect important properties…
Partial coloring, vertex decomposability, and sequentially Cohen-Macaulay simplicial complexes
Jennifer Biermann, Christopher A. Francisco, Huy Tài Hà +1
In attempting to understand how combinatorial modifications alter algebraic properties of monomial ideals, several authors have investigated the process of adding "whiskers" to gra…