Let ∆n,d (resp. ∆′ n,d) be the simplicial complex and the facet ideal In,d =
(x1 . . . xd, xd−k+1 . . . x2d−k, . . . , xn−d+1 . . . xn) (resp. Jn,d = (x1 . . . xd, xd−k+1 . . . x2d−k,
. . . , xn−2d+2k+1 . . . xn−d+2k, xn−d+k+1 . . . xnx1 . . . xk)). When d > 2k + 1, we give the
exact formulas to compute the depth and Stanley depth of quotient rings S/Jn,d and S/In,d t
for all t > 1. When d = 2k, we compute the depth and Stanley depth of quotient rings
S/Jn,d and S/In,d, and give lower bounds for the depth and Stanley depth of quotient rings
S/In,d t for all t > 1.

EB00000002726K

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• DEPTH AND STANLEY DEPTH OF THE FACET IDEALS OF SOME CLASSES OF SIMPLICIAL COMPLEXES