Equivalence classes of permutations modulo excedances
نویسندگان
چکیده
منابع مشابه
Excedances of affine permutations
We introduce an excedance statistic for the group of affine permutations S̃n and determine the generating function of its distribution. The proof involves working with enumerating lattice points in a skew version of the root polytope of type A. We also show that the left coset representatives of the quotient S̃n/Sn correspond to increasing juggling sequences and determine their Poincaré series.
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Motivated by the relations between certain difference statistics and the classical permutation statistics we study permutations whose inversion number and excedance difference coincide. It turns out that these (socalled bi-increasing) permutations are just the 321-avoiding ones. The paper investigates their excedance and descent structure. In particular, we give some combinatorial interpretatio...
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In this paper we prove that among the permutations of length n with i fixed points and j excedances, the number of 321-avoiding ones equals the number of 132-avoiding ones, for all given i, j ≤ n. We use a new technique involving diagonals of non-rational generating functions. This theorem generalizes a recent result of Robertson, Saracino and Zeilberger, for which we also give another, more di...
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We consider several generalizations of the classical γ-positivity of Eulerian polynomials using generating functions and combinatorial theory of continued fractions. For the symmetric group, we prove an expansion formula for inversions and excedances as well as a similar expansion for derangements. We also prove the γ-positivity for Eulerian polynomials of type B and for Eulerian polynomials of...
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ژورنال
عنوان ژورنال: Journal of Combinatorics
سال: 2014
ISSN: 2156-3527,2150-959X
DOI: 10.4310/joc.2014.v5.n4.a4