48 citations · 52 across the 8 of their papers we have counts for
8 papers
On ideals of minors of matrices with indeterminate entries
Mordechai Katzman
This paper has two aims. The first is to study ideals of minors of matrices whose entries are among the variables of a polynomial ring. Specifically, we describe matrices whose ide…
Counting monomials
Mordechai Katzman
This paper presents two enumeration techniques based on Hilbert functions. The paper illustrates these techniques by solving two chessboard problems.
The Betti numbers of forests
Sean Jacques, Mordechai Katzman
This paper produces a recursive formula of the Betti numbers of certain Stanley-Reisner ideals (graph ideals associated to forests). This gives a purely combinatorial definition of…
Uniform Behaviour of the Frobenius closures of ideals generated by regular sequences
Mordechai Katzman, Rodney Y. Sharp
This paper is concerned with ideals in a commutative Noetherian ring of prime characteristic. The main purpose is to show that the Frobenius closures of certain ideals of g…
On the arithmetic of tight closure
Holger Brenner, Mordechai Katzman
We provide a negative answer to an old question in tight closure theory by showing that the containment x^3y^3 \in (x^4,y^4,z^4)^* in K[x,y,z]/(x^7+y^7-z^7) holds for infinitely ma…
The Hilbert series of algebras of Veronese type
Mordechai Katzman
This paper gives a fairly explicit formula for the Hilbert series of algebras of Veronese type.