Asymptotic enumeration of generalized latin rectangles
نویسندگان
چکیده
منابع مشابه
Asymptotic enumeration of Latin rectangles
A k X n Latin rectangle is a k X n matrix with entries from {1,2,.. . , n} such that no entry occurs more than once in any row or column. (Thus each row is a permutation of the integers 1,2,..., n.) Let L(k, n) be the number of k x n Latin rectangles. An outstanding problem is to determine the asymptotic value of L(k, n) as n —• oo, with k bounded by a suitable function of n. The first attack o...
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1. Introduction. The problem of enumerating n by k Latin rectangles was solved formally by MacMahon [4] using his operational methods. For k = 3, more explicit solutions have been given in [1], [2], [3], and [5]. Wile further exact enumeration seems difficult, it is an easy heuristic conjecture that the number of n by k Latin rectangles is asymptotic to (-n!)'cexp (-),CY,). Because of an error,...
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Motivated by the recent proof of the Stanley-Wilf conjecture, we study the asymptotic behavior of the number of permutations avoiding a generalized pattern. Generalized patterns allow the requirement that some pairs of letters must be adjacent in an occurrence of the pattern in the permutation, and consecutive patterns are a particular case of them. We determine the asymptotic behavior of the n...
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We use a greedy probabilistic method to prove that for every > 0, every m × n Latin rectangle on n symbols has an orthogonal mate, where m = (1− )n. That is, we show the existence of a second latin rectangle such that no pair of the mn cells receives the same pair of symbols in the two rectangles.
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The current paper deals with the enumeration and classification of the set SORr,n of self-orthogonal r × r partial Latin rectangles based on n symbols. These combinatorial objects are identified with the independent sets of a Hamming graph and with the zeros of a radical zero-dimensional ideal of polynomials, whose reduced Gröbner basis and Hilbert series can be computed to determine explicitly...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1989
ISSN: 0097-3165
DOI: 10.1016/0097-3165(89)90041-1