Let s and t be variables. Define polynomials {n} in s, t by {0}= 0,{1}= 1, and {n}= s {n–1}+ t {n–
2} for n≥ 2. If s, t are integers then the corresponding sequence of integers is called a Lucas …

We introduce the notion of a Mahonian pair. Consider the set, P⁎, of all words having the
positive integers as alphabet. Given finite subsets S, T⊂ P⁎, we say that (S, T) is a …

The Lucas sequence is a sequence of polynomials in s, t defined recursively by {0\}= 0 0=
0,{1\}= 1 1= 1, and {n\}= s {n-1\}+ t {n-2\} n= s n-1+ t n-2 for n ≥ 2 n≥ 2. On specialization of s …

Given two variables s and t, the associated sequence of Lucas polynomials is defined
inductively by {0}= 0,{1}= 1, and {n}= s {n− 1}+ t {n− 2} for n≥ 2. An integer (eg, a Catalan …

Background: Fibonacci patterns and tubular forms both arose early in the phylogeny of
multicellular organisms. Tubular forms offer the advantage of a regulated internal milieu, and …

We prove a lemma, which we call the Order Ideal Lemma, that can be used to demonstrate a
wide array of log-concavity and log-convexity results in a combinatorial manner using order …

Pomerance established several theorems about the number of integers n for which n+ k
divides the binomial coefficient (2 nn), ka given integer. We conduct a similar inquiry about …

arXiv:1409.8629v1 [math.NT] 30 Sep 2014 The congruence of Wolstenholme and
generalized binomial coefficients related to Lucas Page 1 arXiv:1409.8629v1 [math.NT] 30 …

Abstract In 2020, Bennett, Carrillo, Machacek and Sagan gave a polynomial generalization
of the Narayana numbers and conjectured that these polynomials have positive integer …

Lucas atoms are irreducible factors of Lucas polynomials and they were introduced in\cite
{ST}. The main aim of the authors was to investigate, from an innovatory point of view, when …