Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2024; 61(1): 147-160

Online first article January 17, 2024      Printed January 31, 2024

https://doi.org/10.4134/BKMS.b230066

Copyright © The Korean Mathematical Society.

Depth and Stanley depth of two special classes of monomial ideals

Xiaoqi Wei

Jiangsu University of Technology

Abstract

In this paper, we define two new classes of monomial ideals $I_{l,d}$ and $J_{k,d}$. When $d\geq 2k+1$ and $l\leq d-k-1$, we give the exact formulas to compute the depth and Stanley depth of quotient rings $S/I_{l,d}^{t}$ for all $t\geq 1$. When $d=2k=2l$, we compute the depth and Stanley depth of quotient ring $S/I_{l,d}$. When $d\geq 2k$, we also compute the depth and Stanley depth of quotient ring $S/J_{k,d}$.

Keywords: Monomial ideal, depth, Stanley depth, Stanley conjecture

MSC numbers: 13C15, 13P10, 13F20, 13F55

Supported by: This work was supported by the National Natural Science Foundation of China (No. 12126330).

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