GRACIELA BERBERIÁN,1 CECILIA HIDALGO,2 REINALDO DIPOLO,3 AND LUIS BEAUGÉ1 1Instituto de Investigación Médica Mercedes y Martı́n Ferreyra, 5000 Córdoba, Argentina; 2Centro de Estudios Cientı́ficos de Santiago, Santiago 9; and Departamento de Fisiologı́a y Biofı́sica, Facultad de Medicina, Universidad de Chile, Santiago 7, Chile; and 3Laboratorio de Permeabilidad Iónica, Instituto Venezolano de Inves...

In this paper we will investigate the connection between random matrices and finding the longest increasing subsequence of a permutation. We will introduce a model for the problem using a simple card game. Then we will talk about Young tableaux and their relation to the symmetric group. Representation theory and power-sum symmetric functions serve as the bridge between this combinatorial constr...

A two-rowed array αn = ( a1 a2 . . . an b1 b2 . . . bn ) is said to be in lexicographic order if ak ≤ ak+1 and bk ≤ bk+1 if ak = ak+1. A length ` (strictly) increasing subsequence of αn is a set of indices i1 < i2 < . . . < i` such that bi1 < bi2 < . . . < bi` . We are interested in the statistics of the length of the longest increasing subsequence of αn chosen according to Dn, for distinct fam...

We propose a new nonparametric test for the supposition of independence between two continuous random variables X and Y. Given a sample of (X,Y ), the test is based on the size of the longest increasing subsequence of the permutation which maps the ranks of the X observations to the ranks of the Y observations. We identify the independence assumption between the two continuous variables with th...

We investigate combinatorial enumeration problems related to subsequences of strings; in contrast to substrings, subsequences need not be contiguous. For a finite alphabet Σ, the following three problems are solved. (1) Number of distinct subsequences: Given a sequence s ∈ Σ and a nonnegative integer k ≤ n, how many distinct subsequences of length k does s contain? A previous result by Chase st...

Inspired by the results of Stanley and Widom concerning the limiting distribution of the lengths of longest alternating subsequences in random permutations, and results of Deutsch, Hildebrand and Wilf on the limiting distribution of the longest increasing subsequence for pattern-restricted permutations, we find the limiting distribution of the longest alternating subsequence for pattern-restric...

Given a string S = a1a2a3 · · · an, the longest increasing subsequence (LIS) problem is to find a subsequence of S such that the subsequence is increasing and its length is maximal. In this paper, we propose and solve two variants of the LIS problem. The first one is the minimal height LIS where the height means the difference between the greatest and smallest elements. We propose an algorithm ...

We present a number of results relating partial Cauchy-Littlewood sums, integrals over the compact classical groups, and increasing subsequences of permutations. These include: integral formulae for the distribution of the longest increasing subsequence of a random involution with constrained number of fixed points; new formulae for partial Cauchy-Littlewood sums, as well as new proofs of old f...