Contributions to Discrete Mathematics (E-Journal, University of Calgary)
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Pell Coding and Pell Decoding Methods with Some Applications
Get PDFWe develop a new coding and decoding method using the generalized Pell -numbers for . The relations among the code matrix elements, error detection, and correction have been established for coding theory when . We give two new blocking algorithms using Pell numbers and generalized Pell -numbers for
Total colouring of some cartesian and direct product graphs
No full textA graph is -total colourable if there is an assignment of different colours to the vertices and edges of the graph such that no two adjacent nor incident elements receive the same colour. The total chromatic number of some direct product graphs are determined. In particular, a sufficient condition is given for direct products of bipartite graphs to have total chromatic number equal to its maximum degree plus one. Partial results towards the total chromatic number of are also established
A new mathematical model for tiling finite regions of the plane with polyominoes
Get PDFNote from the editor: On May 11, 2024, an indexing error was found on page 104. This has since been corrected as of June 11, 2024. For more information, please see footnote 3 of page 104.
We present a new mathematical model for tiling finite subsets of using an arbitrary, but finite, collection of polyominoes. Unlike previous approaches that employ backtracking and other refinements of `brute-force\u27 techniques, our method is based on a systematic algebraic approach, leading in most cases to an underdetermined system of linear equations to solve. The resulting linear system is a binary linear programming problem, which can be solved via direct solution techniques, or using well-known optimization routines.
We illustrate our model with some numerical examples computed in MATLAB. Users can download, edit, and run the codes from https://doi.org/10.5281/zenodo.5975482. For larger problems we solve the resulting binary linear programming problem with an optimization package such as CPLEX, GUROBI, or SCIP, before plotting solutions in MATLAB
Closed formulas and identities on the Bell polynomials and falling factorials
Get PDFThe authors establish a pair of closed-form expressions for special values of the Bell polynomials of the second kind for the falling factorials, derive two pairs of identities involving the falling factorials, find an equivalent expression between two special values for the Bell polynomials of the second kind, and present five closed-form expressions for the (modified) spherical Bessel functions
On irreversible spread of influence in edge-weighted graphs
Get PDFVarious kinds of spread of influence occur in real world social and virtual networks. These phenomena are formulated by activation processes and irreversible dynamic monopolies in combinatorial graphs representing the topology of the networks. In most cases, the nature of influence is weighted and the spread of influence depends on the weight of edges. The ordinary formulation and results for dynamic monopolies do not work for such models. In this paper we present a graph theoretical analysis for spread of weighted influence and mention a real world example realizing the activation model with weighted influence. Then we obtain some extremal bounds and algorithmic results for activation process and dynamic monopolies in directed and undirected graphs with weighted edges
-Factorization of and
No full textIn this study, we show that necessary conditions for -factorization of and (complete partite graph with parts of size ) are sufficient. We proved that there exists a -factorization of if and only if and . This result immediately gives that has a -factorization if and only if and
Diameter 3
Get PDFLet be the class of finite metric spaces with nonzero distances in the set omitting triangles of the form and . We prove that the class of linearly ordered structures from satisfies the Ramsey property
Corrigendum to ``"On the enumeration of a class of toroidal graphs" [Contrib. Discrete Math. 13 (2018), no. 1, 79-119]
Get PDFCorrigendum to ``On the enumeration of a class of toroidal graphs [Contrib. Discrete Math. 13 (2018), no. 1, 79-119
Alternating series of Apéry-type for the Riemann zeta function
Get PDFBy making use of a transformation formula for the nonterminating well-poised -series, we investigate a class of alternating series of Apéry-type and establish several identities for the Riemann zeta function, including three identities conjectured by Sun (2015)
The polar of convex lattice sets
Get PDFLet be a convex lattice set in containing the origin as the interior of its convex hull. In this paper, the definition of the polar of a convex lattice set is given both in and . Some properties and inequalities about the convex lattice sets and their polar are established