The length is(w) of the longest increasing subsequence of a permutation w in the symmetric group Sn has been the object of much investigation. We develop comparable results for the length as(w) of the longest alternating subsequence of w, where a sequence a, b, c, d, . . . is alternating if a > b < c > d < · · · . For instance, the expected value (mean) of as(w) for w ∈ Sn is exactly (4n + 1)/6...

We investigate the probability distribution of the length of the second row of a Young diagram of size N equipped with Plancherel measure. We obtain an expression for the generating function of the distribution in terms of a derivative of an associated Fredholm determinant, which can then be used to show that as N → ∞ the distribution converges to the Tracy-Widom distribution [TW] for the secon...

The authors consider the length, lN , of the length of the longest increasing subsequence of a random permutation of N numbers. The main result in this paper is a proof that the distribution function for lN , suitably centered and scaled, converges to the Tracy-Widom distribution [TW1] of the largest eigenvalue of a random GUE matrix. The authors also prove convergence of moments. The proof is ...

We show that a wide variety of generalized increasing subsequence problems admit a one parameter family of extensions for which we can exactly compute the mean length of the longest increasing subsequence. By the nature of the extension, this gives upper bounds on the mean in the unextended model, which turn out to be asymptotically tight for all of the models that have so far been analyzed. A ...

The Malthusian model of population and economic growth has two key components. First, there is a positive effect of the standard of living on the growth rate of population, resulting either from a purely biological effect of consumption on birth and death rates, or a behavioral response on the part of potential parents to their economic circumstances. Second, because of the existence of some fi...

a basic subject in economy is change in growth of population and it’s link to ‎other variables. if growth in population is consistent with other economic ‎circumstances, it would lead to economic growth, otherwise it would be ‎problematic. by using okun&apos;s law and population structures, this paper is ‎analysis the case for iran for 1974-2010. predictions are related to 2025 ‎horizon. the re...

This paper is concerned with certain connections between the ensemble of n × n unitary matrices—specifically the characteristic function of the random variable tr(U)—and combinatorics—specifically Ulam’s problem concerning the distribution of the length of the longest increasing subsequence in permutation groups—and the appearance of Painlevé functions in the answers to apparently unrelated que...

The interplay between two-dimensional percolation growth models and one-dimensional particle processes has been a fruitful source of interesting mathematical phenomena. In this paper we develop a connection between the construction of Busemann functions in the Hammersley last-passage percolation model with i.i.d. random weights, and the existence, ergodicity and uniqueness of equilibrium (or ti...

background: because of the close relationship between economic growth and welfare of the societies many economists have been seeking to identify the sources of economic growth. human capital through enhancing workforce skills and quality, increases the amount of workforce income which consequently leads to economic growth. methods: this study is based on data from the social accounting matrix o...