7 citations · 24 across the 13 of their papers we have counts for
16 papers
Simplicial complexes with many facets are vertex decomposable
Anton Dochtermann, Ritika Nair, Jay Schweig +2
Suppose is a pure simplicial complex on vertices having dimension and let be its codimension in the simplex. Terai and Yoshida proved that if the number of…
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…
The Type Defect of a Simplicial Complex
Hailong Dao, Jay Schweig
Fix a field . When is a simplicial complex on vertices with Stanley-Reisner ideal , we define and study an invariant called the of . Excep…
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…