18 citations · 43 across the 34 of their papers we have counts for
8 papers · 2 filters
Generalized r-Lah numbers
Mark Shattuck
In this paper, we consider a two-parameter polynomial generalization, denoted by G_{a,b}(n,k;r), of the r-Lah numbers which reduces to these recently introduced numbers when a=b=1.…
Generalizations of Bell number formulas of Spivey and Mezo
Mark Shattuck
We provide q-generalizations of Spivey's Bell number formula in various settings by considering statistics on different combinatorial structures. This leads to new identities invol…
A monotonicity property for generalized Fibonacci sequences
Toufik Mansour, Mark Shattuck
Given k>1, let a_n be the sequence defined by the recurrence a_n=c_1a_{n-1}+c_2a_{n-2}+...+c_ka_{n-k} for n>=k, with initial values a_0=a_1=...=a_{k-2}=0 and a_{k-1}= 1. We show un…
Chebyshev Polynomials and Statistics on a New Collection of Words in the Catalan Family
Toufik Mansour, Mark Shattuck
Recently, a new class of words, denoted by L_n, was shown to be in bijection with a subset of the Dyck paths of length 2n having cardinality given by the (n-1)-st Catalan number. H…
Combinatorial Identities for Incomplete Tribonacci Polynomials
Mark Shattuck
The incomplete tribonacci polynomials, denoted by T_n^{(s)}(x), generalize the usual tribonacci polynomials T_n(x) and were introduced in [10], where several algebraic identities w…
Restricted ascent sequences and Catalan numbers
David Callan, Toufik Mansour, Mark Shattuck
Ascent sequences are those consisting of non-negative integers in which the size of each letter is restricted by the number of ascents preceding it and have been shown to be equinu…