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We study the generating function for the number of permutations on n letters containing exactly r > 0 occurrences of 132. It is shown that finding this function for a given r amounts to a routineâ€¦ (More)

- Alexander Burstein, Toufik Mansour
- Electr. J. Comb.
- 2002

We find generating functions for the number of words avoiding certain patterns or sets of patterns with at most 2 distinct letters and determine which of them are equally avoided. We also find exactâ€¦ (More)

- Toufik Mansour
- 2002

Recently, Kitaev [Ki2] introduced partially ordered generalized patterns (POGPs) in the symmetric group, which further generalize the generalized permutation patterns introduced by Babson andâ€¦ (More)

- Toufik Mansour, Yidong Sun
- Eur. J. Comb.
- 2008

Abstract. In this paper we enumerate the number of ways of selecting k objects from n objects arrayed in a line such that no two selected ones are separated by mâˆ’1, 2mâˆ’1, Â· Â· Â· , pmâˆ’1 objects andâ€¦ (More)

- Petter BrÃ¤ndÃ©n, Toufik Mansour
- J. Comb. Theory, Ser. A
- 2005

We say that a word w on a totally ordered alphabet avoids the word v if there are no subsequences in w order-equivalent to v. In this paper we suggest a new approach to the enumeration of words on atâ€¦ (More)

In [GM] Guibert and Mansour studied involutions on n letters avoiding (or containing exactly once) 132 and avoiding (or containing exactly once) an arbitrary pattern on k letters. They alsoâ€¦ (More)

- Toufik Mansour
- 2004

A permutation is said to be alternating if it starts with rise and then descents and rises come in turn. In this paper we study the generating function for the number of alternating permutations on nâ€¦ (More)

We study generating functions for the number of permutations on n letters avoiding 132 and an arbitrary permutation Ï„ on k letters, or containing Ï„ exactly once. In several interesting cases theâ€¦ (More)

- Eric S. Egge, Toufik Mansour
- Electr. J. Comb.
- 2002

Several authors have examined connections between permutations which avoid 132, continued fractions, and Chebyshev polynomials of the second kind. In this paper we prove analogues of some of theseâ€¦ (More)

- Alexander Burstein, Peter HÃ¤stÃ¶, Toufik Mansour
- Electr. J. Comb.
- 2002

In this article we generalize packing density problems from permutations to patterns with repeated letters and generalized patterns. We are able to find the packing density for some classes ofâ€¦ (More)