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COMBINATORICS
1998
13 years 9 months ago
1998
Using Zeilberger’s factorization of two-stack-sortable permutations, we write a functional equation — of a strange sort — that defines their generating function according t...
COMBINATORICS
2002
13 years 9 months ago
2002
Several authors have examined connections between permutations which avoid 132, continued fractions, and Chebyshev polynomials of the second kind. In this paper we prove analogues...
COMBINATORICS
1999
13 years 9 months ago
1999
Abstract. Consider, for a permutation Sk, the number F(n, ) of permutations in Sn which avoid as a subpattern. The conjecture of Stanley and Wilf is that for every there is a c...
COMBINATORICS
2006
13 years 9 months ago
2006
Given an integer s 0 and a permutation Sn, let ,s be the graph on n vertices {1, . . . , n} where two vertices i < j are adjacent if the permutation flips their order and th...
COMBINATORICS
2007
13 years 9 months ago
2007
Suppose xm + axn is a permutation polynomial over Fp, where p > 5 is prime and m > n > 0 and a ∈ F∗ p. We prove that gcd(m−n, p−1) /∈ {2, 4}. In the special cas...