A new infinite family of minimally nonideal matrices
نویسندگان
چکیده
منابع مشابه
A new infinite family of minimally nonideal matrices
Minimally nonideal matrices are a key to understanding when the set covering problem can be solved using linear programming. The complete classification of minimally nonideal matrices is an open problem. One of the most important results on these matrices comes from a theorem of Lehman, which gives a property of the core of a minimally nonideal matrix. Cornuéjols and Novick gave a conjecture on...
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This paper describes a backtracking algorithm for the enumeration of nonisomorphic minimally nonideal (n × n) matrices that are not degenerate projective planes. The application of this algorithm for n ≤ 12 yielded 20 such matrices, adding 5 matrices to the 15 previously known. For greater dimensions, n = 14 and n = 17, 13 new matrices are given. For nonsquare matrices, 38 new minimally nonidea...
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It has been conjectured that iϊ-matrices and even skew iJ-matrices always exist for n divisible by 4. Constructions of both types of matrices have been given for particular values of n and also for various infinite classes of values (see [1] for the pertinent references). In [1] D. Blatt and G. Szekeres constructed for the first time a skew ίf-matrix of order 52. Their construction is summarize...
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Let $mathcal{F}$ be an field of zero characteristic and $N_{infty}(mathcal{F})$ be the algebra of infinite strictly upper triangular matrices with entries in $mathcal{F}$, and $f:N_{infty}(mathcal{F})rightarrow N_{infty}(mathcal{F})$ be a non-additive Lie centralizer of $N_{infty }(mathcal{F})$; that is, a map satisfying that $f([X,Y])=[f(X),Y]$ for all $X,Yin N_{infty}(mathcal{F})...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2011
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2010.09.004