منابع مشابه
Zero-sum Square Matrices
Let A be a matrix over the integers, and let p be a positive integer. A submatrix B of A is zero-sum mod p if the sum of each row of B and the sum of each column of B is a multiple of p. Let M(p, k) denote the least integer m for which every square matrix of order at least m has a square submatrix of order k which is zero-sum mod p. In this paper we supply upper and lower bounds for M(p, k). In...
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For a code C = C(n,M) the level k code of C, denoted Ck, is the set of all vectors resulting from a linear combination of precisely k distinct codewords of C. We prove that if k is any positive integer divisible by 8, and n = γk, M = βk ≥ 2k then there is a codeword in Ck whose weight is either 0 or at most n/2− n( 1 8γ − 6 (4β−2)2 ) + 1. In particular, if γ < (4β − 2) /48 then there is a codew...
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A square matrix is called line-sum-symmetric if the sum of elements in each of its rows equals the sum of elements in the corresponding column. Let A be an n x n nonnegative matrix and let X and Y be n x n diagonal matrices having positive diagonal elements. Then the matrices XA, XAXand XA Yare called a row-scaling, a similarity-scaling and an equivalence-scaling of A. The purpose of this paper...
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We consider integer matrices Nt whose rows are indexed by the t-subsets of an n-set and whose columns are all distinct images of a particular column under the symmetric group Sn. Examples include matrices in the association algebras of the Johnson schemes. Three related problems are addressed. What is the Smith normal form (or a diagonal form) for Nt and the rank of Nt over a field of character...
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For a graph H with at most n vertices and a weighing of the edges of Kn with integers, we seek a copy of H in Kn whose weight is minimal, possibly even zero. Of a particular interest are the cases where H is a spanning subgraph (or an almost spanning subgraph) and the case where H is a fixed graph. In particular, we show that relatively balanced weighings of Kn with {−r, . . . , r} guarantee al...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2002
ISSN: 0195-6698
DOI: 10.1006/eujc.2002.0595