24 citations · 93 across the 24 of their papers we have counts for
8 papers · 1 filter
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…
The problem of the pawns
S. Kitaev, T. Mansour
In this paper we study the number of ways to place nonattacking pawns on an chessboard. We find an upper bound for and analyse its asymptotic behavi…
Squaring the terms of an order linear recurrence
Toufik Mansour
We find an explicit formula for the generating function for the squaring the terms of an order linear recurrence.
A note on sum of k-th power of Horadam's sequence
Toufik Mansour
Let for with and . In this paper we find an explicit expression, in terms of determinants, for for any $k…