We compute the expected number of commutations appearing in a reduced word for the longest element in the symmetric group. The asymptotic behavior of this value is analyzed and shown to approach the length of the permutation, meaning that nearly all positions in the reduced word are expected to support commutations. Finally, we calculate the asymptotic frequencies of commutations, consecutive n...

The asymptotic scaling behavior of the mixing region induced by a random velocity field is determined by applying Corrsin’s hypothesis in both the Eulerian and Lagrangian pictures. Both pictures lead to the same results for the asymptotic scaling exponent of the mixing region. Both longitudinal and transverse diffusion are asymptotically non-Fickian (Fickian) when the correlation function of th...

Knowing the solution to Helmholtz equation in a narrow band, with a width of order wave length around a scatterer, we investigate the possibility to construct the wave fronts predicted by the asymptotic methods Geometrical Optics (GO) and Geometrical Theory of Diffraction (GTD). More specifically we show how to build a polynomial approximation of the asymptotic solution on a circle around the s...

We determine the asymptotic limiting probability as m-->infinity that a random string of length m over some alphabet sigma can be determined uniquely by its substrings of length l. This is an abstraction of a problem faced when trying to sequence DNA clones by SBH.

A construction for a minimal cycle basis for the Cartesian and the strong product of two graphs from the minimal length cycle bases of the factors is presented. Furthermore, we derive asymptotic expressions for the average length of the cycles in the minimal cycle bases of the powers (iterated products) of graphs. In the limit only triangles and squares play a role.

Very odd sequences were introduced in 1973 by Pelikán who conjectured that there were none of length ≥ 5. This conjecture was disproved first by MacWilliams and Odlyzko [17] in 1977 and then by two different sets of authors in 1992 [1], 1995 [9]. We give connections with duadic codes, cyclic difference sets, levels (Stufen) of cyclotomic fields, and derive some new asymptotic results on the len...

In this paper we obtain asymptotic estimates for pairs of closed geodesics on negatively curved manifolds, the differences of whose lengths lie in a prescribed family of shrinking intervals, were the geodesics are ordered with respect to a discrete length. In certain cases, this discrete length can be taken to be the word length with respect to a set of generators for the fundamental group.

This article studies the cardinality of perfect multi deletion binary codes. The lower bound for any code with fixed length and number deletions, asymptotic achievability Levenshtein's upper are shown.

We study conditions for the detection of an N -length iid sequence with unknown pmf p1, among M N -length iid sequences with unknown pmf p0. We show how the quantity M2−N D(p1||p0) determines the asymptotic probability of error.

We show that there is no batch-means estimation procedure for consistently estimating the asymptotic variance when the number of batches is held fixed as the run length increases. This result suggests that the number of batches should increase as the run length increases for sequential stopping rules based on batch means.