Stanley depth of monomial ideals with small number of generators
Keyword(s):
AbstractFor a monomial ideal I ⊂ S = K[x 1...,x n], we show that sdepth(S/I) ≥ n − g(I), where g(I) is the number of the minimal monomial generators of I. If I =νI′, where ν ∈ S is a monomial, then we see that sdepth(S/I) = sdepth(S/I′). We prove that if I is a monomial ideal I ⊂ S minimally generated by three monomials, then I and S/I satisfy the Stanley conjecture. Given a saturated monomial ideal I ⊂ K[x 1,x 2,x 3] we show that sdepth(I) = 2. As a consequence, sdepth(I) ≥ sdepth(K[x 1,x 2,x 3]//I) +1 for any monomial ideal in I ⊂ K[x 1,x 2,x 3].
Keyword(s):
2011 ◽
Vol 48
(2)
◽
pp. 220-226
Keyword(s):
Keyword(s):
2012 ◽
Vol 140
(2)
◽
pp. 493-504
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2019 ◽
Vol 148
(5)
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pp. 1849-1862