How often are two permutations comparable?
نویسندگان
چکیده
منابع مشابه
How Often Are Two Permutations Comparable?
Two permutations of [n] are comparable in the Bruhat order if one is closer, in a natural way, to the identity permutation, 1 2 · · · n, than the other. We show that the number of comparable pairs is of order (n!) /n2 at most, and (n!) (0.708) at least. For the related weak order, the corresponding bounds are (n!) (0.362) and (n!) ∏n i=1 (H (i) /i), where H (i) := ∑i j=1 1/j. In light of numeri...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2008
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-08-04478-4