97 citations · 499 across the 139 of their papers we have counts for
10 papers · 1 filter
A monotonicity property for generalized Fibonacci sequences
Toufik Mansour, Mark Shattuck
Given k>1, let a_n be the sequence defined by the recurrence a_n=c_1a_{n-1}+c_2a_{n-2}+...+c_ka_{n-k} for n>=k, with initial values a_0=a_1=...=a_{k-2}=0 and a_{k-1}= 1. We show un…
Recurrence relations in counting the pattern 13-2 in flattened permutations
Toufik Mansour, David G. L. Wang
We prove that the generating function for the number of flattened permutations having a given number of occurrences of the pattern 13-2 is rational, by using the recurrence relatio…
Log-Concavity of Combinations of Sequences and Applications to Genus Distributions
Jonathan L. Gross, Toufik Mansour, Thomas W. Tucker +1
We formulate conditions on a set of log-concave sequences, under which any linear combination of those sequences is log-concave, and further, of conditions under which linear combi…
Evaluation of spherical GJMS determinants
Toufik Mansour, J. S. Dowker
An expression in the form of an easily computed integral is given for the determinant of the scalar GJMS operator on an odd--dimensional sphere. Manipulation yields a sum formula f…
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…
Some combinatorial arrays related to the Lotka-Volterra system
Shi-Mei Ma, Toufik Mansour, David Callan
The purpose of this paper is to investigate the connection between the Lotka-Volterra system and combinatorics. We study several context-free grammars associated with the Lotka-Vol…