Depth and Stanley depth of the edge ideals of square paths and square cycles
In this paper, we compute depth and Stanley depth for the quotient ring of the edge ideal
associated to a square path on n vertices. We also compute depth and Stanley depth for the
quotient ring of the edge ideal associated to a square cycle on n vertices, when n≡ 0, 3, 4
(mod 5), and give tight bounds when n≡ 1, 2 (mod 5). We also prove a conjecture of Herzog
presented in, for the edge ideals of square paths and square cycles.
associated to a square path on n vertices. We also compute depth and Stanley depth for the
quotient ring of the edge ideal associated to a square cycle on n vertices, when n≡ 0, 3, 4
(mod 5), and give tight bounds when n≡ 1, 2 (mod 5). We also prove a conjecture of Herzog
presented in, for the edge ideals of square paths and square cycles.
Abstract
In this paper, we compute depth and Stanley depth for the quotient ring of the edge ideal associated to a square path on n vertices. We also compute depth and Stanley depth for the quotient ring of the edge ideal associated to a square cycle on n vertices, when n≡0,3,4( mod 5), and give tight bounds when n≡1,2( mod 5). We also prove a conjecture of Herzog presented in , for the edge ideals of square paths and square cycles.
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