Asymptotic Growth of Associated Primes of Certain Graph Ideals

2012/04/15 by Sarah Wolff, Wolff, Sarah
Mathematics · #05C38 #05E99 #13F55 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.CO #msc:05C38 #msc:05E99 #msc:13F55

paper · pdf · doi:10.48550/arxiv.1204.3315

14 pages, 1 figure. In v2, paper had been rewritten. To appear in Communications in Algebra

arxiv created 2012/12/05 · arxiv updated 2012/12/06

Abstract

We specify a class of graphs, H_t, and characterize the irreducible decomposition of all powers of the cover ideals. This gives insight into the structure and stabilization of the corresponding associated primes; specifically, providing an answer to the question "For each integer t≥ 0, does there exist a (hyper) graph H_t such that stabilization of associated primes occurs at s≥ (χ(H_t)-1)+t?" asked by Francisco, Hà, and Van Tuyl. For each t, H_t has chromatic number 3 and associated primes that stabilize at s=2+t.

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