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Paper
IPM / M / 7318 |
School of Mathematics
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Title: |
The minimal free resolution of a class of square-free monomial ideals
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Author(s): |
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Rash. Zaare-Nahandi
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Rah. Zaare-Nahandi
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Status: |
Published
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Journal: |
J. Pure Appl. Algebra
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Vol.: |
189
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Year: |
2004
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Pages: |
263-278
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Supported by: |
IPM
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Abstract: |
For positive integers n,b1 ≤ b2 ≤ … ≤ bn
and t ≤ n, let I1 be the transversal monomial
ideal generated by square-free monomials
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yi1j1yi2j2…yitjt, 1 ≤ i1 < i2 < … < it ≤ n, 1 ≤ jk ≤ bik, k = 1, …, t, |
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where yij 's are distinct indeterminates. It is
observed that the simplicial complex associated to this ideal is
pure shellable if and only if b1=… = bn=1, but its
Alexander dual is always pure and shellable. The simplicial
complex admits some weaker shelling which leads to the computation
of its Hilbert series. The main result is the construction of the
minimal free resolution for the quotient ring of I1. This class
of monomial ideals includes the ideals of t-minors of generic
pluri-circulant matrices under a change of coordinates. The last
family of ideals arise from some specializations of the defining
ideals of generic singularities of algebraic varieties.
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