19 citations · 27 across the 10 of their papers we have counts for
10 papers
Matchings Avoiding Partial Patterns
William Y. C. Chen, Toufik Mansour, Sherry H. F. Yan
We show that matchings avoiding certain partial patterns are counted by the 3-Catalan numbers. We give a characterization of 12312-avoiding matchings in terms of restrictions on th…
Counting occurrences of 3412 in an involution
Toufik Mansour
We study the generating function for the number of involutions on letters containing exactly $r\gs0$ occurrences of 3412. It is shown that finding this function for a given …
Involutions Restricted by 3412, Continued Fractions, and Chebyshev Polynomials
Eric Egge, Toufik Mansour
We study generating functions for the number of involutions, even involutions, and odd involutions in subject to two restrictions. One restriction is that the involution avoi…
Independent sets in certain classes of (almost) regular graphs
Alexander Burstein, Sergey Kitaev, Toufik Mansour
We enumerate the independent sets of several classes of regular and almost regular graphs and compute the corresponding generating functions. We also note the relations between the…
Counting rises, levels, and drops in compositions
Silvia Heubach, Toufik Mansour
A composition of $n\in\NN$ is an ordered collection of one or more positive integers whose sum is . The number of summands is called the number of parts of the composition. A pa…
Finite automata and pattern avoidance in words
Petter Brändén, Toufik Mansour
We say that a word on a totally ordered alphabet avoids the word if there are no subsequences in order-equivalent to . In this paper we suggest a new approach to the…