The Permanent Rank of a Matrix
نویسندگان
چکیده
منابع مشابه
Note on the Permanent Rank of a Matrix
De ne the perrank of a matrix A to be the size of a largest square submatrix of A with nonzero permanent. Motivated in part by the Alon-Jaeger-Tarsi Conjecture [3], we prove several results on perranks.
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It is known that any square matrix A of size n over a field of prime characteristic p that has rank less than n/(p− 1) has a permanent that is zero. We give a new proof involving the invariant Xp. There are always matrices of any larger rank with non-zero permanents. It is shown that when the rank of A is exactly n/(p − 1), its permanent may be factorized into two functions involving Xp. Let n ...
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abstract in this thesis at first we comput the determinant of hankel matrix with enteries a_k (x)=?_(m=0)^k??((2k+2-m)¦(k-m)) x^m ? by using a new operator, ? and by writing and solving differential equation of order two at points x=2 and x=-2 . also we show that this determinant under k-binomial transformation is invariant.
15 صفحه اولPermanent rank and transversals
We use the polynomial method of Alon to give a sufficient condition for the existence of partial transversals in terms of the permanent rank of a certain matrix.
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In this paper, the notion of rank-k numerical range of rectangular complex matrix polynomials are introduced. Some algebraic and geometrical properties are investigated. Moreover, for ϵ > 0; the notion of Birkhoff-James approximate orthogonality sets for ϵ-higher rank numerical ranges of rectangular matrix polynomials is also introduced and studied. The proposed denitions yield a natural genera...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1999
ISSN: 0097-3165
DOI: 10.1006/jcta.1998.2904