Pólya's Permanent Problem
نویسندگان
چکیده
منابع مشابه
Pólya's Permanent Problem
A square real matrix is sign-nonsingular if it is forced to be nonsingular by its pattern of zero, negative, and positive entries. We give structural characterizations of sign-nonsingular matrices, digraphs with no even length dicycles, and square nonnegative real matrices whose permanent and determinant are equal. The structural characterizations, which are topological in nature, imply polynom...
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In Valiant’s theory of arithmetic complexity, the classes VP and VNP are analogs of P and NP. A fundamental problem concerning these classes is the Permanent and Determinant Problem: Given a field F of characteristic 6= 2, and an integer n, what is the minimum m such that the permanent of an n × n matrix X = (xij) can be expressed as a determinant of an m × m matrix, where the entries of the de...
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The size of an arithmetical formula is the number of symbols (+,×) which it contains. The complexity of a polynomial defined over a field k is the minimum size of formulas defining it (see [10]). Using this notion of complexity, Valiant gave algebraic analogs to algorithmic complexity problems such as P = NP (see [10, 11, 12]). In this context, we would like to find lower bounds to the complexi...
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The Permanent versus Determinant problem is the following: Given an n × n matrix X of indeterminates over a field of characteristic different from two, find the smallest matrix M whose coefficients are linear functions in the indeterminates such that the permanent of X equals the determinant of M. We prove that the dimensions of M are at most 2n − 1. The determinant and the permanent of an (n ×...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2004
ISSN: 1077-8926
DOI: 10.37236/1832