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A simple characterization of special matchings in lower Bruhat intervals
We give a simple characterization of special matchings in lower Bruhat
intervals (that is, intervals starting from the identity element) of a Coxeter
group. As a byproduct, we obtain some results on the action of special
matchings.Comment: accepted for publication on Discrete Mathematic
The Complexity of Testing Monomials in Multivariate Polynomials
The work in this paper is to initiate a theory of testing monomials in
multivariate polynomials. The central question is to ask whether a polynomial
represented by certain economically compact structure has a multilinear
monomial in its sum-product expansion. The complexity aspects of this problem
and its variants are investigated with two folds of objectives. One is to
understand how this problem relates to critical problems in complexity, and if
so to what extent. The other is to exploit possibilities of applying algebraic
properties of polynomials to the study of those problems. A series of results
about and polynomials are obtained in this paper,
laying a basis for further study along this line
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