6 papers · 1 filter
Inversions in Random Permutations Under the Ewens Sampling Distribution With and Without a Prescribed Number of Fixed Points
Ross G. Pinsky, Dominic T. Schickentanz
In the first part of the paper, we study the inversion statistic of random permutations under the family of Ewens sampling distributions on . W…
A family of non-uniform distributions on the set of parking functions generated by random permutations
Ross G. Pinsky
We introduce a rather natural family of non-uniform distributions on , , the set of parking functions of length . One of the motivations for this comes fro…
The inversion statistic in derangements and in other permutations with a prescribed number of fixed points
Ross G. Pinsky
We study how the inversion statistic is influenced by fixed points in a permutation. %The expected number of inversions in a uniformly random permutation in is $\frac{n(n-1)}…
The distribution on permutations induced by a random parking function
Ross G. Pinsky
A parking function on creates a permutation in via the order in which the cars appear in the parking spaces. Placing the uniform probability measure on the set…
Mean and variance of the longest alternating subsequence in a random separable permutation
Ross G. Pinsky
A permutation is \it separable \rm if it can be obtained from the singleton permutation by iterating direct sums and skew sums. Equivalently, it is separable if and only it avoids…
Large deviations for the longest alternating and the longest increasing subsequence in a random permutation avoiding a pattern of length three
Ross G. Pinsky
We calculate the large deviations for the length of the longest alternating subsequence and for the length of the longest increasing subsequence in a uniformly random permutation t…