Related papers: On Simultaneous Palindromes

For a vertex set $S\subseteq V(G)$ in a graph $G$, the {\em distance multiset}, $D(S)$, is the multiset of pairwise distances between vertices of $S$ in $G$. Two vertex sets are called {\em homometric} if their distance multisets are…

Algorithmic computation in polynomial rings is a classical topic in mathematics. However, little attention has been given to the case of rings with an infinite number of variables until recently when theoretical efforts have made possible…

A persistence module $M$, with coefficients in a field $\mathbb{F}$, is a finite-dimensional linear representation of an equioriented quiver of type $A_n$ or, equivalently, a graded module over the ring of polynomials $\mathbb{F}[x]$. It is…

Higgs doublets may come in three generations. The scalar sector of the resulting three-Higgs-doublet model (3HDM) may be constrained by global symmetry groups $G$ leading to characteristic phenomenology. There exists the full list of…

Despite the fact that almost all real numbers are absolutely normal---that is, the digits in their expansions to any base occur in all possible configurations with the expected frequency---not one specific example of an absolutely normal…

We prove a number of results on the structure and enumeration of palindromes and antipalindromes. In particular, we study conjugates of palindromes, palindromic pairs, rich words, and the counterparts of these notions for antipalindromes.

Let $p_n$ be the number of partitions of an integer $n$. For each of the partition statistics of counting their parts, ranks, or cranks, there is a natural family of integer polynomials. We investigate their asymptotics and the limiting…

Let $B$ be a set of Eulerian subgraphs of a graph $G$. We say $B$ forms a $k$-basis if it is a minimum set that generates the cycle space of $G$, and any edge of $G$ lies in at most $k$ members of $B$. The basis number of a graph $G$,…

A palindromic periodicity is a factor of an infinite word $(ps)^\omega$ where $p$ and $s$ are palindromes and the factor has length at least $|ps|$, for example, $accabaccab$. In this paper we describe several ways in which a palindromic…

In this paper, we show that there are only finitely many Narayana's numbers which can be written as product of three repdigits in base $g$ with $g \geq 2$. Moreover, for $2 \leq g \leq 10$, we determine all these numbers.

Interpolation theory for complex polynomials is well understood. In the non-commutative quaternionic setting, the polynomials can be evaluated "on the left" and "on the right". If the interpolation problem involves interpolation conditions…

To represent positive integers by regular patterns on a plane or in three-dimensional space may be traced back to the Pythagoreans. The aim of the present article is to explore the possibility of extending the representation framework for…

For a large integer $m,$ we obtain an asymptotic formula for the number of solutions of a certain congruence modulo $m$ with four variables, where the variables belong to special sets of residue classes modulo $m.$ This formula are applied…

A set of positive integers $A$ is called a $B_{h}[g]$ set if there are at most $g$ different sums of $h$ elements from $A$ with the same result. This definition has a generalization to abelian groups and the main problem related to this…

Consider the sets of integers $A$ that avoid any arrangement of $g$ congruent $h$-subsets. Our findings refine and improve upon some results by Erd\H{o}s and Harzheim about these sets.

For any fixed measure $H$ that maps graphs to real numbers, the MinH problem is defined as follows: given a graph $G$, an integer $k$, and a target $\tau$, is there a set $S$ of $k$ vertices that can be deleted, so that $H(G - S)$ is at…

A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by no more than one other edge (and any pair of crossing edges cross only once). A non-1-planar graph $G$ is minimal if the graph $G-e$ is 1-planar for every…

Let $p$ be a prime number, and $h$ a positive integer such that $\gcd(p,h)=1$. We prove, without invoking Dirichlet's theorem, that the arithmetic progression $p\left(\mathbf{N}\cup \{0\}\right)+h$ contains infinitely many prime numbers.…

Let PG be the Proth-Gilbreath operator that transforms a sequence of integers into the sequence of the absolute values of the differences between all pairs of neighbor terms. Consider the infinite tables obtained by successive iterations of…

The set A of nonnegative integers is called a basis of order h if every nonnegative integer can be represented as the sum of exactly h not necessarily distinct elements of A. An additive basis A of order h is called thin if there exists c >…