We propose the first algebraic determinantal formula to enumerate random rhombus tilings filling a centro-symmetric octagon of any size. This result uses the GesselViennot technique and generalizes to any octagon a former specialized formula by Elnitsky.

Abstract. In this paper we enumerate the number of ways of selecting k objects from n objects arrayed in a line such that no two selected ones are separated bym−1, 2m−1, · · · , pm−1 objects and provide three different formulas when m, p ≥ 1 and n ≥ pm(k − 1). Also, we prove that the number of ways of selecting k objects from n objects arrayed in a circle such that no two selected ones are sepa...

A very detailed segmentation of prosodic phrase was carried out in order to construct a Japanese prosodic database. Boundaries correspond to junctures between phrases including C|C and V|V clusters. The "prosodic phrase" we introduced as a unit of the segmentation was defined and regarded as a unit of language speech perception. For the exact segmentation, the wide-band spectrum, the narrow-ban...

The study examined the extent to which Performance Evaluation affects employee job satisfaction in a federal government agency Nigeria. This adopts quantitative technique as primary data was gathered through validated instrument. approach relied on total enumeration sampling technique, with Population equal sample size (275). inferential statistical tool is Partial Least Square-Structural Equat...

In this study, a microcolony technique was combined with direct fluorescent antibody staining for the specific detection and enumeration of Legionella pneumophila in freshwater samples with growth activity. This method allowed the detection of active L. pneumophila (within 48 h) in 91 bath water samples collected from 30 bathing facilities, with similar sensitivity of a conventional plate-count...

The direct double-agar-layer plaque assay for the detection and enumeration of specific bacteriophages of Bacteroides fragilis from contaminated-water samples was performed. Several factors that affect the methods, such as conditions of the bacterial culture, composition of the assay medium, addition of divalent cations, and decontamination techniques applied to the sample, were evaluated. The ...

Let g = g0 ⊕ g1 be a simple Z2-graded Lie algebra and let b0 be a fixed Borel subalgebra of g0. We describe and enumerate the abelian b0-stable subalgebras of g1.

We enumerate the connected graphs that contain a linear number of edges with respect to the number of vertices. So far, only first term of the asymptotics and a bound on the error were known. Using analytic combinatorics, i.e. generating function manipulations, we derive the complete asymptotic expansion. keywords. connected graphs, analytic combinatorics, generating functions, asymptotic expan...

We study a special partial fraction technique which is designed for rational functions with poles on the unit circle, known as q-fractions. Even though the theory of q-partial fractions has already been applied to the Rademacher Conjecture, no systematic computational development appeared. In this paper we present two algorithms for the computation of q-partial fractions and highlight certain p...