Results 41 to 50 of about 302 (115)

A new class of infinite products, and Euler′s totient

International Journal of Mathematics and Mathematical Sciences, Volume 17, Issue 3, Page 417-422, 1994., 1993
We introduce some new infinite products, the simplest being where ϕk is the set of positive integers less than and relatively prime to k, valid for |y|∧|qy| both less than unity, with q ≠ 1. The idea of a q‐analogue for the Euler totient function is suggested.
Geoffrey B. Campbell
wiley   +1 more source

An infinite version of the Pólya enumeration theorem

International Journal of Mathematics and Mathematical Sciences, Volume 15, Issue 4, Page 697-700, 1992., 1991
Using measure theory, the orbit counting form of Pólya′s enumeration theorem is extended to countably infinite discrete groups.
Robert A. Bekes
wiley   +1 more source

Snow Leopard Permutations and Their Even and Odd Threads [PDF]

Discrete Mathematics & Theoretical Computer Science, 2016
Caffrey, Egge, Michel, Rubin and Ver Steegh recently introduced snow leopard permutations, which are the anti-Baxter permutations that are compatible with the doubly alternating Baxter permutations. Among other things, they showed that these permutations
Eric S. Egge, Kailee Rubin
doaj   +1 more source

On Hilbert polynomial of certain determinantal ideals

International Journal of Mathematics and Mathematical Sciences, Volume 14, Issue 1, Page 155-162, 1991., 1989
Let X = (Xij) be an m(1) by m(2) matrix whose entries Xij, 1 ≤ i ≤ m(1), 1 ≤ j ≤ m(2); are indeterminates over a field K. Let K[X] be the polynomial ring in these m(1)m(2) variables over K. A part of the second fundamental theorem of Invariant Theory says that the ideal I[p + 1] in K[X], generated by (p + 1) by (p + 1) minors of X is prime.
Shrinivas G. Udpikar
wiley   +1 more source

MacMahon’s statistics on higher-dimensional partitions

Forum of Mathematics, Sigma, 2023
We study some combinatorial properties of higher-dimensional partitions which generalize plane partitions. We present a natural bijection between d-dimensional partitions and d-dimensional arrays of nonnegative integers.
Alimzhan Amanov, Damir Yeliussizov
doaj   +1 more source

On coefficients of circuit polynomials and characteristic polynomials

International Journal of Mathematics and Mathematical Sciences, Volume 8, Issue 4, Page 697-705, 1985., 1985
Results are given from which expressions for the coefficients of the simple circuit polynomial of a graph can be obtained in terms of subgraphs of the graph. From these are deduced parallel results for the coefficients of the characteristic polynomial of a graph.
E. J. Farrell
wiley   +1 more source

On the number of vertices of each rank in phylogenetic trees and their generalizations [PDF]

Discrete Mathematics & Theoretical Computer Science, 2016
We find surprisingly simple formulas for the limiting probability that the rank of a randomly selected vertex in a randomly selected phylogenetic tree or generalized phylogenetic tree is a given integer.
Miklós Bóna
doaj   +1 more source

Path decompositions of chains and circuits

International Journal of Mathematics and Mathematical Sciences, Volume 6, Issue 3, Page 521-533, 1983., 1983
Expressions for the path polynomials (see Farrell [1]) of chains and circuits are derived. These polynomials are then used to deduce results about node disjoint path decompositions of chains and circuits. Some results are also given for decompositions in which specific paths must be used.
E. J. Farrell
wiley   +1 more source

Equivalence classes of functions on finite sets

International Journal of Mathematics and Mathematical Sciences, Volume 5, Issue 4, Page 745-762, 1982., 1982
By using Pólya′s theorem of enumeration and de Bruijn′s generalization of Pólya′s theorem, we obtain the numbers of various weak equivalence classes of functions in RD relative to permutation groups G and H where RD is the set of all functions from a finite set D to a finite set R, G acts on D and H acts on R.
Chong-Yun Chao, Caroline I. Deisher
wiley   +1 more source

A generalization of the dichromatic polynomial of a graph

International Journal of Mathematics and Mathematical Sciences, Volume 4, Issue 4, Page 725-729, 1981., 1981
The Subgraph polynomial fo a graph pair (G, H), where H⫅G, is defined. By assigning particular weights to the variables, it is shown that this polynomial reduces to the dichromatic polynomial of G. This idea of a graph pair leads to a dual generalization of the dichromatic polynomial.
E. J. Farrell
wiley   +1 more source