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Given two nonincreasing integral vectors R and S, with the same sum, we denote by A(R, S) the class of all (0, 1)-matrices with row sum vector R, and column sum vector S. The Bruhat order and the Secondary Bruhat order on A(R, S) are both extensions of the classical Bruhat order on S n , the symmetric group of degree n. These two partial orders are not, in general, the same. In this paper we prove that if R = (2, 2, . . . , 2) or R = (1, 1, . . . , 1), then the Bruhat order and the Secondary Bruhat order coincide on A(R, S).

We state a necessary and sufficient condition for equality of two nonzero decomposable symmetrized tensors when the symmetrizer is associated with an irreducible character of the symmetric group of degree m.

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