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Counting k-ary words by number of adjacency differences of a prescribed size
Sela Fried, Toufik Mansour, Mark Shattuck
Recently, the general problem of enumerating permutations such that for all , where and are fixed, was considered by…
Hessenberg-Toeplitz Matrix Determinants with Schroder and Fine Number Entries
Taras Goy, Mark Shattuck
In this paper, we find determinant formulas of several Hessenberg-Toeplitz matrices whose nonzero entries are derived from the small and large Schroder and Fine number sequences. A…
Enumeration of non-crossing partitions according to subwords with repeated letters
Mark Shattuck
An avoidance pattern where the letters within an occurrence of which are required to be adjacent is referred to as a subword. In this paper, we enumerate members of the set NC_n of…
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…