منابع مشابه
Perfect divisibility and 2-divisibility
A graph G is said to be 2-divisible if for all (nonempty) induced subgraphs H of G, V (H) can be partitioned into two sets A,B such that ω(A) < ω(H) and ω(B) < ω(H). A graph G is said to be perfectly divisible if for all induced subgraphs H of G, V (H) can be partitioned into two sets A,B such that H[A] is perfect and ω(B) < ω(H). We prove that if a graph is (P5, C5)-free, then it is 2-divisibl...
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We address two sets of long-standing open questions in linear algebra and probability theory, from a computational complexity perspective: stochastic matrix divisibility, and divisibility and decomposability of probability distributions. We prove that finite divisibility of stochastic matrices is an NP-complete problem, and extend this result to nonnegative matrices, and completely-positive tra...
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Bipartitional relations were introduced by Foata and Zeilberger in their characterization of relations which give rise to equidistribution of the associated inversion statistic and major index. We consider the natural partial order on bipartitional relations given by inclusion. We show that, with respect to this partial order, the bipartitional relations on a set of size [Formula: see text] for...
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For given integers a, b and j ≥ 1 we determine the set R (j) a,b of integers n for which a n − b is divisible by n . For j = 1, 2, this set is usually infinite; we determine explicitly the exceptional cases for which a, b the set R (j) a,b (j = 1, 2) is finite. For j = 2, we use Zsigmondy’s Theorem for this. For j ≥ 3 and gcd(a, b) = 1, R (j) a,b is probably always finite; this seems difficult ...
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It is shown that the coset lattice of a finite group has shellable order complex if and only if the group is complemented. Furthermore, the coset lattice is shown to have a Cohen–Macaulay order complex in exactly the same conditions. The group theoretical tools used are relatively elementary, and avoid the classification of finite simple groups and of minimal finite simple groups. © 2006 Elsevi...
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ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2017
ISSN: 0895-4801,1095-7146
DOI: 10.1137/15m1049142