Showing papers in "Advances in Applied Mathematics in 2007"

TL;DR: It is proved that in the long time limit, the probability that the PASEP is in a particular configuration @t is essentially the generating function for permutation tableaux of shape @l(@t) enumerated according to three statistics.

TL;DR: In this article, the authors introduced the notion of crossings and nestings of permutations and showed how this is related to the stationary distribution of the partially asymmetric exclusion process (PASEP) model.

TL;DR: It is given new sufficient conditions for a sequence of polynomials to have only real zeros based on the method of interlacing zeros, and settles certain conjectures of Stahl on genus polynmials by proving them for certain classes of graphs.

TL;DR: It is shown that the log-convexity is preserved under componentwise sum, under binomial convolution, and by the linear transformations given by the matrices of binomial coefficients and Stirling numbers of two kinds.

TL;DR: If the authors think of nxn permutation matrices as transversals of the n by n square diagram, then this result can be generalised to transversal of Young diagrams.

TL;DR: In this paper, the authors present an algorithm that computes all possible minimal wiring diagrams for a given set of state transition measurements, using primary decomposition of monomial ideals as the principal tool.

TL;DR: It is shown that yet another pair of statistics exists, and whose joint distribution constitutes a ''natural'' solution to Foata's problem.

TL;DR: This work proves classification and realization theorems for state complexes, using CAT(0) geometry as the primary tool, for reconfiguration problems in robotics, biology, computer science, combinatorics, and group theory.

TL;DR: In this paper, the Furedi-Hajnal problem was extended to hypergraphs with ordered vertex sets and it was shown that the number of 1-entries in a hypergraph with side length n which avoids a d-dimensional permutation matrix is O(n^d^-^1).

TL;DR: The main result is a limit shape theorem for the two-dimensional surface defined by a uniform random nxn square Young tableau, which leads to a calculus of variations minimization problem that resembles the minimization problems studied by Logan-Shepp, Vershik-Kerov, and Cohn-Larsen-Propp.

TL;DR: In this paper, the limiting behavior of the Euler polynomials was studied and it was shown that scaled zeros are uniformly distributed under a conformal transformation, and when linearly scaled, they approach a definite curve in the complex plane related to the Szego curve.

TL;DR: Basic hypergeometric series identities are revisited systematically by means of Abel's lemma on summation by parts, and several new formulae and transformations are established.

TL;DR: A new identity for the product of two partial theta functions is proved and an immediate corollary is Warnaar's generalization of the Jacobi triple product identity.

TL;DR: The proof reveals that more general proofs for the existence of @e-equilibria in stochastic games must involve the topological structure of how the equilibria of one-stage games are related to changes in the payoffs.

TL;DR: The surface area of an ellipsoid in E^n is studied as the function of the lengths of the semi-axes and an explicit formula as an integral over S^n^-^1 is given to derive convexity properties of the surface area.

TL;DR: An algorithm called striped matrix elimination is presented which is asymptotically faster than traditional Gauss-Jordan elimination, and the exact distribution of the complexity for matrices from GL"n(F"q), with n and q small is determined.

TL;DR: The purpose of this paper is to compute the Mobius function of filters in the partition lattice formed by restricting to partitions by type and the permutahedron makes a cameo appearance.

TL;DR: This paper proves Chapoton's conjecture on the duality formula: Q"n(x,y,z,t)=Q"n (x+nz+nt,y,-t,-z), and answers his question about the combinatorial interpretation of Q" n.

TL;DR: The results are extended to the case of weaker inclusions: If the inhomogeneities inside the body are more (or less) conductive than the known background, and if the conductivity coefficient and its m-1 lowest normal derivatives are continuous over the inclusion boundaries, then the factorization method provides an explicit characterization of the inclusions.

TL;DR: This paper reviews Euler-Maclaurin formulas for a polytope, uses an algebraic formalism due to Cappell and Shaneson to relate the different formulas, and presents proofs of the exact formulas obtained.

TL;DR: The fundamental solutions of the Heat and sub-Laplace equations for these anisotropic groups are presented and some estimates for them are obtained, which may be useful.

TL;DR: This work uses nonsmooth analysis to investigate whether the presence of multiple parameters allows a faster asymptotic convergence rate, and argues that for a specific parameterization, it does not, at least locally.

TL;DR: Two kinds of decompositions of a D-module are introduced in this article, a Loewy-decomposition and a primary decomposition which rely on the concept of the D- module of relative syzygies introduced in the paper.

TL;DR: In this paper, it was shown that two quantities relating to the length of permutations defined on trees are independent of the structures of trees and that these results are closely related to the results obtained by Graham and Pollak [R.L. Graham, H.O. Pollak, and J.J. Neumann.

TL;DR: A kinematic technique is used to prove a Bonnesen-type inequality for the Euclidean sphere and the hyperbolic plane, having constant Gauss curvature @k 0.

TL;DR: This work uses elementary methods and operator identities to solve linear matrix differential equations and obtains explicit formulas for the exponential of a matrix and gives explicit constructions of solutions of scalar homogeneous equations with certain initial values.

TL;DR: The Kauffman brackets of rational links as a typical link family are investigated, an explicit formula using transfer matrix approach is obtained, and another link family is provided to point out that the relation built actually can be used to deal with Kauff man brackets of all such link families.

TL;DR: It is proved that the periodic function mentioned above is nowhere differentiable, which means that the expansions from right to left can be computed by translating the ordinary binary expansion using a (finite state) transducer.

TL;DR: A general bibasic summation formula determined by such two functions f(x,y) and g(x-y) as well as four arbitrary sequences is obtained which unifies the bibalicious summation formulas of Gasper and Rahman, Chu, and Macdonald.

TL;DR: A key feature of the method that leads to a fast algorithm is to combine generating functions with the Laplace transform to compute explicitly the entries of the matrix without numerical integration.