Depth and sdepth of powers of the path ideal of a cycle graph. II - BĂLĂNESCU, Silviu; CIMPOEAȘ, Mircea (Studia Universitatis Babeș-Bolyai Mathematica, 2025)
Let Jn,m := (x1x2 · · · xm, x2x3 · · · xm+1, . . . , xn−m+1 · · · xn, xn−m+2 · · · xnx1, . . . , xnx1 · · · xm−1) be the m-path ideal of the cycle graph of length n, in the ring of polynomials S = K[x1, . . . , xn]. As a continuation of our previous paper, we prove several new results regarding depth(S/ Jnt,m) and sdepth(S/Jnt,m), where t ≥ 1. Mathematics Subject Classification (2010): 13C15, 13P10, 13F20. Received 01 May 2025; Accepted 01 October 2025.