7 citations · 8 across the 29 of their papers we have counts for
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On Gotzmann thresholds and a conjecture of Bonanzinga and Eliahou
Trung Chau
We obtain a recursive formula for the Gotzmann threshold of a power of a variable. Consequently, we give an affirmative answer to a conjecture of Bonanzinga and Eliahou.
Scarf complexes of connected and path ideals
Trung Chau, Richie Sheng, Tim Tribone +1
The -connected ideal of a graph is generated by all connected induced subgraphs of with vertices. When , this coincides with the usual edge ideal of the graph…
From neural codes to homological invariants: regularity and projective dimension of polarized neural ideals
Trung Chau
Neural codes form an algebraic framework to study the nervous system, and understanding neural codes is a key goal of mathematical neuroscience. Neural rings and ideals are the too…
Projective monomial curves associated to numerical semigroups with multiplicity , width , and embedding dimension
Om Prakash Bhardwaj, Trung Chau, Omkar Javadekar
Numerical semigroups with multiplicity , width , and embedding dimension are of the form $$S(e,m,n) = \langle \{e, e+1, \ldots, 2e-1\} \setminus \{e+m, e+n\} \rangle,…
Admissible set and squarefree-power-like function with applications to squarefree symbolic powers
Trung Chau, Kanoy Kumar Das, Amit Roy +1
We introduce the abstract notion of squarefree-power-like functions, which unify the sequences of squarefree ordinary and symbolic powers of squarefree monomial ideals. By employin…
The -singularities of algebras defined by permanents
Trung Chau
Let be a matrix of indeterminates, an integer, and define the ideal generated by the permanents of all submatrix of . is called a permanent…
Extremal behavior of ideals of minors
Trung Chau, Michael DeBellevue, Souvik Dey +2
Let be either a fiber product or an artinian stretched Gorenstein ring, with in the latter case. We prove that the…
Maximal minors of -generic matrices have rational singularities
Trung Chau, Manoj Kummini
We show that the quotient ring by the ideal of maximal minors of a -generic matrix has rational singularities. This answers a conjecture of Eisenbud (1988) that such rings are n…
Trees whose path ideals have linear quotients
Trung Chau, Kanoy Kumar Das, Animikha Dutta Dhar +2
For any integer , we classify all trees whose -path ideals have linear quotients.
Permanental ideals of symmetric matrices
Trung Chau
In this article, we study the ideal generated by permanents of a symmetric matrix. We denote this ideal by where is a symmetric matrix. We compute a Gröbne…
Admissible matchings and the Castelnuovo-Mumford regularity of square-free powers
Trung Chau, Kanoy Kumar Das, Amit Roy +1
Let be any square-free monomial ideal, and denote the hypergraph associated with . Refining the concept of -admissible matching of a graph defined by Erey…
Homological invariants of edge ideals of weighted oriented graphs
Trung Chau, Richie Sheng, Deborah Wooton
We determine all possible triples of depth, dimension, and regularity of edge ideals of weighted oriented graphs with a fixed number of vertices. Also, we compute all the possible…
The Scarf complex of squarefree powers, symbolic powers of edge ideals, and cover ideals of graphs
Trung Chau, Nursel Erey, Aryaman Maithani
Every monomial ideal has a Scarf complex, which is a subcomplex of its minimal free resolution. We say that is Scarf if its Scarf complex is also its minimal free resolutio…
Edge ideals with linear quotients and without homological linear quotients
Trung Chau, Kanoy Kumar Das, Aryaman Maithani
A monomial ideal is said to have homological linear quotients if for each , the homological shift ideal has linear quotients. It is a well-known fac…
Realizing resolutions of powers of extremal ideals
Trung Chau, Art M. Duval, Sara Faridi +3
Extremal ideals are a class of square-free monomial ideals which dominate and determine many algebraic invariants of powers of all square-free monomial ideals. For example, the $r^…
Minimal cellular resolutions of monomial ideals with five generators and their Artinian reductions
Trung Chau
We prove that monomial ideals with at most five generators and their Artinian reductions have minimal generalized Barile-Macchia resolutions. As a corollary, these ideals have mini…