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Open Journal of Discrete Mathematics (OJDM) is an openly accessible journal published quarterly. The goal of this journal is to provide a platform for scientists and academicians all over the world to promote,share,and discuss various new issues and developments in different areas of discrete mathematics. All manuscri…
Catalin Nitica, Viorel Nitica
Let b ≥ 2 be a numeration base. A b -weak additive Ramanujan-Hardy (or b -wARH) number N is a non-negative integer for which there exists at least one non-negative integer A , such that the sum of A and the sum of base b digits of N , added to the reversal of…
Nathan Thomas Hamlin
The author recently published a paper which claimed that an ordinal interpretation of numbers had limited applicability for cryptography. A further examination of this subject, in particular to what extent an ordinal interpretation is useful for recurrence se…
Ramy Shaheen, Ziad Kanaya, Khaled Alshehada
Let G be a graph and k be a positive integer. We consider a game with two players Alice and Bob who alternate in coloring the vertices of G with a set of k colors. In every turn, one vertex will be chosen by one player. Alice’s goal is to color all vertices w…
David Ariyibi, Kevin Chang, Pamela E. Harris
We define and study the Extended Feline Josephus Game, a game in which n players, each with ℓ lives, stand in a circle. The game proceeds by alternating between hitting k consecutive players—each of whom will consequently lose a life—and skipping s cons…
Shih-Wei Chao, Matthew Macauley
In 1986, G.X. Viennot introduced the theory of heaps of pieces as a visualization of Cartier and Foata’s “partially commutative monoids”. These are essentially labeled posets satisfying a few additional properties, and one natural setting where they arise is…
Khalil Tawbe, Salwa Mansour, 1 1
This paper uses the theoretical material developed in a previous study by the authors in order to reconstruct a subclass of 2-convex polyominoes called where the upper left corner and the lower right corner of the polyomino contain each only one cell. The mai…
Ramy Shaheen, Mohammad Assaad, Ali Kassem
In the eternal dominating set problem, guards form a dominating set on a graph and at each step, a vertex is attacked. We consider the “all guards move” of the eternal dominating set problem. In which one guard has to move to the attacked vertex and all the r…
Viorel Niţică, Premalata Junius
Motivated by their intrinsic interest and by applications to the study of numeric palindromes and other sequences of integers, we discover infinite sets of solutions and almost solutions of the equation N ⋅ M =reversal ( N ⋅ M ) . Most of our result…
Shiv Gupta
The polynomial x 4 +1 is irreducible in Ζ [x] but is locally reducible, that is, it factors modulo p for all primes p . In this paper we investigate this phenomenon and prove that for any composite natural number N there are monic irreducible polynomials…
Khalil Tawbe, Nadine Ghandour, Ali Atwi
A polyomino P is called 2-convex if for every two cells there exists a monotone path included in P with at most two changes of direction. This paper studies the geometrical properties of a sub-class of 2-convex polyominoes called where the upper left corner a…
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Open Journal of Discrete Mathematics (OJDM) is an openly accessible journal published quarterly. The goal of this journal is to provide a platform for scientists and academicians all over the world to promote,share,and discuss various new issues and developments in different areas of discrete mathematics. All manuscri… All articles are open access under a CC BY 4.0 licence, with authors retaining copyright.
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