Related papers: Two classes of modular $p$-Stanley sequences

We obtain explicit expressions for the class in the Grothendieck group of varieties of the moduli space of genus 0 stable curves with n marked points. This information is equivalent to the Poincar\'e polynomial; it implies explicit…

Let S=K[x_1,...,x_n] be a polynomial ring. Denote by $p_a$ the power sum symmetric polynomial x_1^a+...+x_n^a. We consider the following two questions: Describe the subsets $A \subset \mathbb{N}$ such that the set of polynomials $p_a$ with…

In this paper, we suggest a lower and an upper bound for the Generalized Fibonacci-p-Sequence, for different values of p. The Fibonacci-p-Sequence is a generalization of the Classical Fibonacci Sequence. We first show that the ratio of two…

A sequence $S=s_{1}s_{2}..._{n}$ is \emph{nonrepetitive} if no two adjacent blocks of $S$ are identical. In 1906 Thue proved that there exist arbitrarily long nonrepetitive sequences over 3-element set of symbols. We study a generalization…

In 1991, N. Shalaby conjectured that any additive group $\mathbb{Z}_n$, where $n\equiv1$ or 3 (mod 8) and $n \geq11$, admits a strong Skolem starter and constructed these starters of all admissible orders $11\leq n\leq57$. Shalaby and et…

We define the notion of basic set data for finite groups (building on the notion of basic set, but including an order on the irreducible characters as part of the structure), and we prove that the Springer correspondence provides basic set…

A Sturmian sequence is an infinite nonperiodic string over two letters with minimal subword complexity. In two papers, the first written by Morse and Hedlund in 1940 and the second by Coven and Hedlund in 1973, a surprising correspondence…

Recursive saturation and resplendence are two important notions in models of arithmetic. Kaye, Kossak, and Kotlarski introduced the notion of arithmetic saturation and argued that recursive saturation might not be as rigid as first assumed.…

In a recent paper, Bilu et al. studied a conjecture of Marques and Lengyel on the $p$-adic valuation of the Tribonacci sequence. In this article, we study the $p$-adic valuation of third order linear recurrence sequences by considering a…

In this paper we provide a way to construct new moment sequences from a given moment sequence. An operator based on multivariate positive polynomials is applied to get the new moment sequences. A class of new sequences is corresponding to a…

A classical problem in analytic number theory is to study the distribution of $\alpha p$ modulo 1, where $\alpha$ is irrational and $p$ runs over the set of primes. We consider the subsequence generated by the primes $p$ such that $p+2$ is…

Let Y be a random variable whose moment generating function exists in a neighborhood of the origin. Recently, probabilistic Stirling numbers of the first kind and of the second kind associated with Y have been introduced. However,…

We construct Steiner triple systems without parallel classes for an infinite number of orders congruent to $3 \pmod{6}$. The only previously known examples have order $15$ or $21$.

Years ago Zeev Rudnick defined the ${\lambda}$-Poisson generic sequences as the infinite sequences of symbols in a finite alphabet where the number of occurrences of long words in the initial segments follow the Poisson distribution with…

This article introduces a new kind of number systems on $p$-adic integers which is inspired by the well-known $3n+1$ conjecture of Lothar Collatz. A $p$-adic system is a piecewise function on $\mathbb{Z}_p$ which has branches for all…

We establish a lower bound of 2/p(p-1) for the asymptotic density of the Motzkin numbers divisible by a general prime number p > 3. We provide a criteria for when this asymptotic density is actually 1. We also provide a partial…

We establish existence theorems for the image of the normalized character map of the $p$-adic Heisenberg algebra $S$ taking values in the algebra of Serre $p$-adic modular forms $M_p$. In particular, we describe the construction of an…

This work brings techniques from the theory of recurrent integer sequences to the problem of balancedness of symmetric Boolean functions. In particular, the periodicity modulo $p$ ($p$ odd prime) of exponential sums of symmetric Boolean…

Let $p$ be a prime number. A chain $\{p,2p+1,4p+3,\cdots,(p+1)2^{l(p)-1}-1\}$ is called the Cunningham chain generated by $p$ if all elements are prime number and $(p+1)2^{l(p)}-1$ is composite. Then $l(p)$ is called the length of the…

Each finite $p$-perfect group $G$ ($p$ a prime) has a universal central $p$-extension. For a perfect group these central extensions come from its {\sl Schur multiplier}. Serre gave a Stiefel-Whitney class approach to analyzing spin covers…