منابع مشابه
Permutation statistics on involutions
In this paper we look at polynomials arising from statistics on the classes of involutions, In, and involutions with no fixed points, Jn, in the symmetric group. Our results are motivated by F. Brenti’s conjecture [3] which states that the Eulerian distribution of In is logconcave. Symmetry of the generating functions is shown for the statistics d, maj and the joint distribution (d, maj). We sh...
متن کاملMore Statistics on Permutation Pairs
Two inversion formulas for enumerating words in the free monoid by θ-adjacencies are applied in counting pairs of permutations by various statistics. The generating functions obtained involve refinements of bibasic Bessel functions. We further extend the results to finite sequences of permutations. ∗This work is partially supported by EC grant CHRX-CT93-0400 and PRC Maths-Info †Financial suppor...
متن کاملPermutation Statistics on the Alternating Group
Let An ⊆ Sn denote the alternating and the symmetric groups on 1, . . . , n. MacMahaon’s theorem [11], about the equi-distribution of the length and the major indices in Sn, has received far reaching refinements and generalizations, by Foata [5], Carlitz [3, 4], FoataSchützenberger [6], Garsia-Gessel [7] and followers. Our main goal is to find analogous statistics and identities for the alterna...
متن کاملAsymptotic Normality of Statistics on Permutation Tableaux
Abstract. In this paper we use a probabilistic approach to derive the expressions for the characteristic functions of basic statistics defined on permutation tableaux. Since our expressions are exact, we can identify the distributions of basic statistics (like the number of unrestricted rows, the number of rows, and the number of 1s in the first row) exactly. In all three cases the distribution...
متن کاملOn Permutation Statistics and Hecke Algebra Characters
Irreducible characters of Hecke algebras of type A may be represented as reened counts of simple statistics on suitable subsets of permutations. Such formulas have been generalized to characters of other Coxeter groups and their Hecke algebras and to coinvariant algebras. In this paper we present several formulas, applications to combinatorial identities, and related problems. New results are g...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2007
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2005.07.014