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...

by shouldering the burden of a big chunk of global production, and giving shelter to half of the world’s population, currently cities play an important role in national economies. benefits of agglomeration in cities have played a major role in the process of economic development of different countries, however, the expansion of urbanization has produced some problems including environmental and...

rapid urban population is widely known as the main inducement of growing cities in terms of quantity and variety in form. however, the city expansion entails physical challenges and it has profound impacts on the issue of urban morphology. it raises global awareness beyond the urbanism and includes sociology, psychology, economics as well as environmental studies due to the implications of broa...

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...