Complete intersection dimensions and Foxby classes

A note on intersection dimensions of graph classes

Abstract: The intersection dimension of a graph G with respect to a class A of graphs is the minimum k such that G is the intersection of some k graphs on the vertex set V (G) belonging to A. In this paper we follow [ Kratochv́ıl J., Tuza Z.: Intersection dimensions of graph classes, Graphs and Combinatorics 10 (1994), 159– 168 ] and show that for some pairs of graph classes A, B the intersectio...

New Classes of Set-theoretic Complete Intersection Monomial Ideals

Let ∆ be a simplicial complex and χ be an s-coloring of ∆. Biermann and Van Tuyl have introduced the simplicial complex ∆χ. As a corollary of Theorems 5 and 7 in their 2013 article, we obtain that the Stanley–Reisner ring of ∆χ over a field is Cohen–Macaulay. In this note, we generalize this corollary by proving that the Stanley–Reisner ideal of ∆χ over a field is set-theoretic complete interse...

Intersection Theory Classes 20 and 21: Bivariant Intersection Theory

Characteristic Classes, Chern Classes and Applications to Intersection Theory

This is a report for my summer REU program at the University of Chicago, 2014. I would like to acknowledge my mentor Sean Howe in this program for his generous guidance on learning the subject and writing this article, Professor J.P. May who runs this REU program successfully and made my wonderful experience possible, and Professor M. Yan who has encouraged me ever since my first year in colleg...

Toric complete intersection codes

In this paper we construct evaluation codes on zero-dimensional complete intersections in toric varieties and give lower bounds for their minimum distance. This generalizes the results of Gold–Little–Schenck and Ballico–Fontanari who considered evaluation codes on complete intersections in the projective space.