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Permutation statistics on the . . .
, 2008
"... Let An ⊆ Sn denote the alternating and the symmetric groups on 1,...,n. MacMahaon’s theorem [11], about the equidistribution of the length and the major indices in Sn, has received far reaching refinements and generalizations, by Foata [5], Carlitz [3, 4], FoataSchützenberger [6], GarsiaGessel [7 ..."
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Gessel [7] and followers. Our main goal is to find analogous statistics and identities for the alternating group An. A new statistic for Sn, the delent number, is introduced. This new statistic is involved with new Sn equidistribution identities, refining some of the results in [6] and [7]. By a certain
Permutation Statistics of Indexed Permutations
, 1994
"... The definitions of descent, excedance, major index, inversion index and Denert's statistic for the elements of the symmetric group S d are generalized to indexed permutations, i.e. the elements of the group S n d := Z n o S d , where o is wreath product with respect to the usual action of S d ..."
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Cited by 51 (2 self)
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The definitions of descent, excedance, major index, inversion index and Denert's statistic for the elements of the symmetric group S d are generalized to indexed permutations, i.e. the elements of the group S n d := Z n o S d , where o is wreath product with respect to the usual action
EULERIAN CALCULUS ARISING FROM PERMUTATION STATISTICS
, 2014
"... calculus arising from permutation statistics ..."
Algorithms for Permutation Statistics
, 2011
"... Two sequences u, v of n positive integers are order isomorphic if ui < uj if and only if vi < vj for all pairs (i, j) ∈ {1, 2,..., n} 2. A permutation π = π(1)π(2) · · · π(n) ∈ Sn is said to contain σ ∈ Sk as a pattern if there is some ktuple 1 ≤ i1 < i2 < · · · < ik ≤ n such ..."
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Cited by 3 (3 self)
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statistic is a function f: ⋃ n Sn → C. The primary permutation statistics studied in this work are written in terms of the number of copies of a given pattern or patterns. The central concern of this thesis is to compute answers to problems of the following type: “Given patterns σ (1) ,..., σ (t
On the Asymptotic Theory of Permutation Statistics
 Mathematical Methods of Statistics
, 1999
"... : In this paper limit theorems for the conditional distributions of linear test statistics are proved. The assertions are conditioned on the #field of permutation symmetric sets. Limit theorems are proved both for the conditional distributions under the hypothesis of randomness and under general co ..."
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Cited by 24 (2 self)
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: In this paper limit theorems for the conditional distributions of linear test statistics are proved. The assertions are conditioned on the #field of permutation symmetric sets. Limit theorems are proved both for the conditional distributions under the hypothesis of randomness and under general
An Eulerian permutation statistic and generalizations
, 2012
"... Recently, the second author studied an Eulerian statistic (called cover) in the context of convex polytopes, and proved an equal joint distribution of (cover,des) with (des, exc). In this paper, we present several direct bijective proofs that cover is Eulerian, and examine its generalizations and th ..."
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Recently, the second author studied an Eulerian statistic (called cover) in the context of convex polytopes, and proved an equal joint distribution of (cover,des) with (des, exc). In this paper, we present several direct bijective proofs that cover is Eulerian, and examine its generalizations
Permutation Statistics of Indexed and Poset Permutations
"... The definitions of descents and excedances in the elements of the symmetric group S d are generalized in two different directions. First, descents and excedances are defined for indexed permutations, i.e. the elements of the group S n d = Z n o S d , where o is wreath product with respect to the u ..."
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Cited by 11 (3 self)
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The definitions of descents and excedances in the elements of the symmetric group S d are generalized in two different directions. First, descents and excedances are defined for indexed permutations, i.e. the elements of the group S n d = Z n o S d , where o is wreath product with respect
PERMUTATION STATISTICS AND MULTIPLE PATTERN AVOIDANCE
"... Abstract. For a set of permutation patterns Π, let F stn (Π, q) be the stpolynomial of permutations avoiding all patterns in Π. Suppose 312 ∈ Π. For a class of permutation statistics which includes inversion and descent statistics, we give a formula that expresses F stn (Π; q) in terms of these st ..."
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Abstract. For a set of permutation patterns Π, let F stn (Π, q) be the stpolynomial of permutations avoiding all patterns in Π. Suppose 312 ∈ Π. For a class of permutation statistics which includes inversion and descent statistics, we give a formula that expresses F stn (Π; q) in terms
Results 1  10
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1,282