We describe a simple one-person card game, patience sorting. Its analysis leads to a broad circle of ideas linking Young tableaux with the longest increasing subsequence of a random permutation via the Schensted correspondence. A recent highlight of this area is the work of Baik-Deift-Johansson which yields limiting probability laws via hard analysis of Toeplitz determinants.

In this paper, we consider parallel algorithms for the patience sorting and the longest increasing subsequence. These two problems are related each other and are not known to be in the class NC or P -complete. We first propose two algorithms for the patience sorting of n distinct integers. The first algorithm runs in O(m(np + logn)) time using p processors on the EREW PRAM, where m is the numbe...

In this review paper we consider the polynuclear growth (PNG) model in one spatial dimension and its relation to random matrix ensembles. For curved and flat growth the scaling functions of the surface fluctuations coincide with limit distribution functions coming from certain Gaussian ensembles of random matrices. This connection can be explained via point processes associated to the PNG model...

In recent work of Baik, Deift and Rains convergence of moments was established for the limiting joint distribution of the lengths of the first k rows in random Young tableaux. The main difficulty was obtaining a good estimate for the tail of the distribution and this was accomplished through a highly nontrival Riemann-Hilbert analysis. Here we give a simpler derivation. The same method is used ...

Consider a large number n of neurons, each being connected to approximately N other ones, chosen at random. When a neuron spikes, which occurs randomly at some rate depending on its electric potential, its potential is set to a minimum value vmin, and this initiates, after a small delay, two fronts on the (linear) dendrites of all the neurons to which it is connected. Fronts move at constant sp...

The purpose of this dissertation is to study certain classes of permutations and plane partitions of truncated shapes. We establish some of their enumerative and combinatorial properties. The proofs develop methods and interpretations within various fields of algebraic combinatorics, most notably the theory of symmetric functions and their combinatorial properties. The first chapter of this the...

The realisation of Global Cellular Automaton (GCA) using a comparatively high number of communicating finite state machines (FSM) leads to high communication effort. Inside configurable architectures, fixed numbers of FSM and fixed bus widths result in a granularity that makes mapping of larger GCA to these architectures even more difficult. This approach presents a configurable architecture to...

The paper establishes a computational enclosure of the solution of a nonlinear complementarity problem x ≥ 0, l(x) ≥ 0, x l(x) = 0, where l(x) = Mx+ Φ(x) is a so-called almost linear mapping with an H-matrix M with positive diagonal elements and an increasing diagonal mapping Φ. The procedure also delivers a simple proof for the uniqueness of the solution. Mathematics Subject Classification (20...