TY - JOUR

T1 - Hypergraphs with high projective dimension and 1-dimensional hypergraphs

AU - Lin, K. N.

AU - Mantero, P.

N1 - Publisher Copyright:
© 2017 World Scientific Publishing Company.

PY - 2017/9/1

Y1 - 2017/9/1

N2 - (Dual) hypergraphs have been used by Kimura, Rinaldo and Terai to characterize squarefree monomial ideals J with pd(R/J) ≤ μ(J) - 1, i.e. whose projective dimension equals the minimal number of generators of J minus 1. In this paper, we prove sufficient and necessary combinatorial conditions for pd(R/J) ≤ μ(J) - 2. The second main result is an effective explicit procedure to compute the projective dimension of a large class of 1-dimensional hypergraphs (the ones in which every connected component contains at most one cycle). An algorithm to compute the projective dimension is also provided. Applications of these results are given; they include, for instance, computing the projective dimension of monomial ideals whose associated hypergraph has a spanning Ferrers graph.

AB - (Dual) hypergraphs have been used by Kimura, Rinaldo and Terai to characterize squarefree monomial ideals J with pd(R/J) ≤ μ(J) - 1, i.e. whose projective dimension equals the minimal number of generators of J minus 1. In this paper, we prove sufficient and necessary combinatorial conditions for pd(R/J) ≤ μ(J) - 2. The second main result is an effective explicit procedure to compute the projective dimension of a large class of 1-dimensional hypergraphs (the ones in which every connected component contains at most one cycle). An algorithm to compute the projective dimension is also provided. Applications of these results are given; they include, for instance, computing the projective dimension of monomial ideals whose associated hypergraph has a spanning Ferrers graph.

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U2 - 10.1142/S0218196717500291

DO - 10.1142/S0218196717500291

M3 - Article

AN - SCOPUS:85028330850

SN - 0218-1967

VL - 27

SP - 591

EP - 617

JO - International Journal of Algebra and Computation

JF - International Journal of Algebra and Computation

IS - 6

ER -