Ayesha Asloob Qureshi

Ideals generated by 2-minors, collections of cells and stack polyominoes

Abstract In this paper we study ideals generated by quite general sets of 2-minors of an m × n -matrix of indeterminates. The sets of 2-minors are defined by collections of cells and include 2-sided ladders. For convex collections of cells it is shown that the attached ideal of 2-minors is a Cohen–Macaulay prime ideal. Primality is also shown for collections of cells whose connected components are row or column convex. Finally the class group of the ring attached to a stack polyomino and its canonical class is computed, and a classification of the Gorenstein stack polyominoes is given.

The binomial edge ideal of a pair of graphs

We introduce a class of ideals generated by a set of 2-minors of an ( m × n )-matrix of indeterminates indexed by a pair of graphs. This class of ideals is a natural common generalization of binomial edge ideals and ideals generated by adjacent minors. We determine the minimal prime ideals of such ideals and give a lower bound for their degree of nilpotency. In some special cases we compute their Grobner basis and characterize unmixedness and Cohen–Macaulayness.

Alexander duality for monomial ideals associated with isotone maps between posets

For a pair

Ideals Generated by Diagonal 2-Minors

(P,Q)

POLARIZATION OF KOSZUL CYCLES WITH APPLICATIONS TO POWERS OF EDGE IDEALS OF WHISKER GRAPHS

of finite posets the generators of the ideal

Persistence and stability properties of powers of ideals

L(P,Q)

Regularity of Join-meet Ideals of Distributive Lattices

correspond bijectively to the isotone maps from

Simple polyominoes are prime

P

Gröbner bases of balanced polyominoes

to

Nonsimple polyominoes and prime ideals

Q