Author pages are created from data sourced from our academic publisher partnerships and public sources.

Publications Influence

Pattern avoidance in inversion sequences

- T. Mansour, M. Shattuck
- Mathematics
- 1 December 2015

Abstract A permutation of length n may be represented, equivalently, by a sequence a1a2 • • • an satisfying 0 < ai < i for all z, which is called an inversion sequence. In analogy to the usual case… Expand

27 7- PDF

Counting humps and peaks in generalized Motzkin paths

- T. Mansour, M. Shattuck
- Computer Science, Mathematics
- Discret. Appl. Math.
- 1 September 2013

TLDR

10 4

Some enumerative results related to ascent sequences

- T. Mansour, M. Shattuck
- Computer Science, Mathematics
- Discret. Math.
- 16 July 2012

TLDR

18 3- PDF

Some Wilf-equivalences for vincular patterns

- Andrew M. Baxter, M. Shattuck
- Mathematics
- 27 September 2013

We prove several Wilf-equivalences for vincular patterns of length 4, some of which generalize to infinite families of vincular patterns. We also present functional equations for the generating… Expand

10 2- PDF

A general two-term recurrence and its solution

- T. Mansour, S. Mulay, M. Shattuck
- Mathematics, Computer Science
- Eur. J. Comb.
- 2012

TLDR

14 2- PDF

Combinatorial proofs of some Simons-type binomial coefficient identities.

- M. Shattuck
- Mathematics
- 2007

In this note, we present combinatorial proofs of some Moriarty-type binomial coe! cient identities using linear and circular domino arrangements.

8 2- PDF

Combinatorial trigonometry with Chebyshev polynomials

- A. Benjamin, Larry Ericksen, Pallavi Jayawant, M. Shattuck
- Mathematics
- 1 August 2010

We provide a combinatorial proof of the trigonometric identity cosðny Þ¼ TnðcosyÞ, where Tn is the Chebyshev polynomial of the first kind. We also provide combinatorial proofs of other trigonometric… Expand

18 2- PDF

A $$q$$-analog of the hyperharmonic numbers

- T. Mansour, M. Shattuck
- Mathematics
- 1 March 2014

Recently, the $$q$$-analog of the harmonic numbers obtained by replacing each positive integer $$n$$ with $$n_q$$ has been shown to satisfy congruences which generalize Wolstenholme’s theorem. Here,… Expand

7 2

Counting Peaks and Valleys in a Partition of a Set

- T. Mansour, M. Shattuck
- Mathematics
- 2010

A partitionof the set (n) = {1,2,...,n} is a collection {B1,B2,...,Bk} of nonempty disjoint subsets of (n) (called blocks) whose union equals (n). In this paper, we find an explicit formula for the… Expand

2 2- PDF

On a New Family of Generalized Stirling and Bell Numbers

- T. Mansour, M. Schork, M. Shattuck
- Mathematics, Computer Science
- Electron. J. Comb.
- 31 March 2011

TLDR

34 1

...

1

2

3

4

5

...