Connections between longest increasing subsequences in random permutations and eigenvalues of random matrices with complex entries have been intensely studied. This note applies properties of random elements of the finite general linear group to obtain results about the longest increasing subsequence in non-uniform random permutations.

BACKGROUND To decrease the gulf between academic and community perspectives, there has been an increased call among stakeholder groups to collaborate in solving complex urban health problems. Despite these recent shifts, however, community partners face barriers to participate in conferences, ultimately limiting exchange of ideas and uptake of research data. This paper reports on the evaluation...

This paper finds and analyzes a formula for the total variation distance between iterations of riffle shuffles and iterations of “cut and then riffle shuffle”. This allows one to obtain information about the convergence rate of permutation statistics (such as the length of the longest increasing subsequence or position of a given card) under these processes. Similar results are given for affine...

Abstract. We compute the limit distribution for (centered and scaled) length of the longest increasing subsequence of random colored permutations. The limit distribution function is a power of that for usual random permutations computed recently by Baik, Deift, and Johansson (math.CO/9810105). In two–colored case our method provides a different proof of a similar result by Tracy and Widom about...

We prove a formula for the number of permutations in Sn such that their first n−k entries are increasing and their longest increasing subsequence has length n − k. This formula first appeared as a consequence of character polynomial calculations in the work of Adriano Garsia, [2]. We give an elementary proof of this result and also of its q-analogue. In [2], Adriano Garsia derived as a conseque...

Collaboration can provide benefits to the individual and the group across a variety of contexts. Even in simple perceptual tasks, the aggregation of individuals' personal information can enable enhanced group decision-making. However, in certain circumstances such collaboration can worsen performance, or even expose an individual to exploitation in economic tasks, and therefore a balance needs ...

Education Vouchers: The Right to Choose or to Own? M. H. Hassani Shalmaani, Ph.D. Using education vouchers is one way of increasing parental access to schools and hence, creating rightful choices for them in regard to schools. Since such rights require governmental cooperation, it is necessary to delineate the boundaries of parental rights in order to clarify if the parents have s...