For positive integers n_{,}b_{1} ≤ b_{2} ≤ … ≤ b_{n}
and t ≤ n_{,} let I_{1} be the transversal monomial
ideal generated by squarefree monomials
y_{i1j1}y_{i2j2}…y_{it}j_{t}, 1 ≤ i_{1} < i_{2} < … < i_{t} ≤ n_{,} 1 ≤ j_{k} ≤ b_{ik}, k = 1, …, t, 

where y_{ij} 's are distinct indeterminates. It is
observed that the simplicial complex associated to this ideal is
pure shellable if and only if b_{1}=… = b_{n}=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 I_{1}. This class
of monomial ideals includes the ideals of tminors of generic
pluricirculant 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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