3 papers
math.AC2025
Comparing the -number and -polynomials of edge ideals
Kamalesh Saha, Adam Van Tuyl
In this paper, we compare the -numbers and the degree of the -polynomials associated with edge ideals of connected graphs. We prove that the -number can…
math.RA2025
Sign patterns which require or allow the strong multiplicity property
Abhilash Saha, Leona Tilis, Kevin N. Vander Meulen +1
We initiate a study of sign patterns that require or allow the non-symmetric strong multiplicity property (nSMP). We show that all cycle patterns require the nSMP, regardless of th…
math.AC2024
Partial Betti splittings with applications to binomial edge ideals
A. V. Jayanthan, Aniketh Sivakumar, Adam Van Tuyl
We introduce the notion of a partial Betti splitting of a homogeneous ideal, generalizing the notion of a Betti splitting first given by Francisco, HÃ , and Van Tuyl. Given a homog…