1 citations · 1 across the 4 of their papers we have counts for
4 papers
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…
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…
On avoidance of patterns of the form σ-τ by words over a finite alphabet
Toufik Mansour, Mark Shattuck
Vincular or dashed patterns resemble classical patterns except that some of the letters within an occurrence are required to be adjacent. We prove several infinite families of Wilf…