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- W2997409812 abstract "Abstract Let k be a positive integer. We compute depth and Stanley depth of the quotient ring of the edge ideal associated to the k th power of a path on n vertices. We show that both depth and Stanley depth have the same values and can be given in terms of k and n . If n ≣0, k + 1, k + 2, . . . , 2 k (mod(2 k + 1)), then we give values of depth and Stanley depth of the quotient ring of the edge ideal associated to the k th power of a cycle on n vertices and tight bounds otherwise, in terms of n and k . We also compute lower bounds for the Stanley depth of the edge ideals associated to the k th power of a path and a cycle and prove a conjecture of Herzog for these ideals." @default.
- W2997409812 created "2020-01-10" @default.
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- W2997409812 date "2019-12-01" @default.
- W2997409812 modified "2023-10-16" @default.
- W2997409812 title "Depth and Stanley depth of the edge ideals of the powers of paths and cycles" @default.
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- W2997409812 doi "https://doi.org/10.2478/auom-2019-0037" @default.
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