Abstract
In this paper, the signs of the terms in the Laplace expansions of determinants are investigated. The problem is equivalent to that of the parity of the distinguished coset representatives for the (maximal) parabolic subgroups of the symmetric groups. The number of positive and negative terms (equivalently, the number of even and odd representatives) are given explicitly together with their generating functions. Also mentioned are some applications to the symbolic method (in invariant theory) and combinatorics.
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