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.

Researchers suggest that inadequate sanitation contributes to high rates of diarrheal disease causing 20 percent of diarrhea deaths (approximately 280,000 deaths in 2012)i. Despite the billions of dollars that governments and multi-lateral donors are spending on sanitation programming around the developing world, there is still disagreement on the fundamental reasons for high rates of inadequat...

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...

Millions of people travel every day by car in cities around the world, with daily mobility being one main contributors to CO2 emissions. Bicycle-sharing systems are a alternative cars that may help reduce and GHG We analyze public bike-sharing service (BIZI, Zaragoza, Spain, May 2008–August 2019, 24 million uses), from perspective both efficiency demand profiles, determine whether use bicycles ...