Signed Permutation Statistics

Upper Binomial Posets and Signed Permutation Statistics

Permutation patterns and statistics

Call two sequences of distinct integers a1a2 . . . ak and b1b2 . . . bk order isomorphic if they have the same pairwise comparisons, i.e., ai < aj if and only if bi < bj for all indices i, j. For example 132 and 475 are order isomorphic since both begin with the smallest element, have the largest element second, and end with the middle sized element. Let Sn be the set of all permutations of {1,...

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...

Permutation Statistics of Indexed Permutations

The deenitions of descent, excedance, major index, inversion index and Denert's statistic for the elements of the symmetric group S d are generalized It is shown, bijectively, that excedances and descents are equidistributed, and the corresponding descent polynomial, analogous to the Eulerian polynomial , is computed as the f {eulerian polynomial of a simple polynomial. The descent polynomial i...

More 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...