Results 31 to 40 of about 302 (115)

Determinantal generating functions of colored spanning forests

International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 6, Page 273-283, 2004., 2004
The color type of a spanning forest of a graph with colored edges is defined and, subsequently, it is proved that the generating function of such spanning forests is obtained as the formal expansion of a certain determinant. An analogous determinantal expansion yields the generating function of all spanning forests of a given color type that contain a ...
Gregory M. Constantine, Marius G. Buliga
wiley   +1 more source

Generalized orbifold Euler characteristic of symmetric products and equivariant Morava K-theory [PDF]

, 2001
We introduce the notion of generalized orbifold Euler charac- teristic associated to an arbitrary group, and study its properties. We then calculate generating functions of higher order (p-primary) orbifold Euler characteristic of symmetric products of a
Hirotaka Tamanoi
semanticscholar   +1 more source

Counting occurrences of 132 in an even permutation

International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 25, Page 1329-1341, 2004., 2004
We study the generating function for the number of even (or odd) permutations on n letters containing exactly r ≥ 0 occurrences of a 132 pattern. It is shown that finding this function for a given r amounts to a routine check of all permutations in 𝔖2r.
Toufik Mansour
wiley   +1 more source

First hitting times of simple random walks on graphs with congestion points

International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 30, Page 1911-1922, 2003., 2003
We derive the explicit formulas of the probability generating functions of the first hitting times of simple random walks on graphs with congestion points using group representations.
Mihyun Kang
wiley   +1 more source

Equivalence classes of mesh patterns with a dominating pattern [PDF]

Discrete Mathematics & Theoretical Computer Science, 2018
Two mesh patterns are coincident if they are avoided by the same set of permutations, and are Wilf-equivalent if they have the same number of avoiders of each length.
Murray Tannock, Henning Ulfarsson
doaj   +1 more source

Combinatorics of geometrically distributed random variables: new q‐tangent and q‐secant numbers

International Journal of Mathematics and Mathematical Sciences, Volume 24, Issue 12, Page 825-838, 2000., 2000
Up‐down permutations are counted by tangent (respectively, secant) numbers. Considering words instead, where the letters are produced by independent geometric distributions, there are several ways of introducing this concept; in the limit they all coincide with the classical version. In this way, we get some new q‐tangent and q‐secant functions.
Helmut Prodinger
wiley   +1 more source

n‐Color partitions with weighted differences equal to minus two

International Journal of Mathematics and Mathematical Sciences, Volume 20, Issue 4, Page 759-768, 1997., 1997
In this paper we study those n‐color partitions of Agarwal and Andrews, 1987, in which each pair of parts has weighted difference equal to −2 Results obtained in this paper for these partitions include several combinatorial identities, recurrence relations, generating functions, relationships with the divisor function and computer produced tables.
A. K. Agarwal, R. Balasubrananian
wiley   +1 more source

Descent c-Wilf Equivalence [PDF]

Discrete Mathematics & Theoretical Computer Science, 2017
Let $S_n$ denote the symmetric group. For any $\sigma \in S_n$, we let $\mathrm{des}(\sigma)$ denote the number of descents of $\sigma$, $\mathrm{inv}(\sigma)$ denote the number of inversions of $\sigma$, and $\mathrm{LRmin}(\sigma)$ denote the number of
Quang T. Bach, Jeffrey B. Remmel
doaj   +1 more source

Bivariate Chromatic Polynomials of Mixed Graphs [PDF]

Discrete Mathematics & Theoretical Computer Science, 2023
The bivariate chromatic polynomial $\chi_G(x,y)$ of a graph $G = (V, E)$, introduced by Dohmen-P\"{o}nitz-Tittmann (2003), counts all $x$-colorings of $G$ such that adjacent vertices get different colors if they are $\le y$. We extend this notion to
Matthias Beck, Sampada Kolhatkar
doaj   +1 more source

Bicomplex generalized k-Horadam quaternions

Miskolc Mathematical Notes, 2019
This study provides a broad overview of the generalization of the various quaternions, especially in the context of its enhancing importance in the disciplines of mathematics and physics.
Y. Yazlık, Sure Köme, Cahit Köme
semanticscholar   +1 more source