Signed Permutation Statistics and Cycle Type

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,...

On the tenacity of cycle permutation graph

A special class of cubic graphs are the cycle permutation graphs. A cycle permutation graph Pn(α) is defined by taking two vertex-disjoint cycles on n vertices and adding a matching between the vertices of the two cycles.In this paper we determine a good upper bound for tenacity of cycle permutation graphs.

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...

on the tenacity of cycle permutation graph

a special class of cubic graphs are the cycle permutation graphs. a cycle permutation graph pn(α) is defined by taking two vertex-disjoint cycles on n vertices and adding a matching between the vertices of the two cycles.in this paper we determine a good upper bound for tenacity of cycle permutation graphs.