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- Maximillian M. Murphy, Vincent Vatter
- Electr. J. Comb.
- 2002

It is known that the set of permutations, under the pattern containment ordering, is not a partial well-order. Characterizing the partially well-ordered closed sets (equivalently: down sets orâ€¦ (More)

- Sophie Huczynska, Vincent Vatter
- Electr. J. Comb.
- 2006

We introduce and characterise grid classes, which are natural generalisations of other well-studied permutation classes. This characterisation allows us to give a new, short proof of the Fibonacciâ€¦ (More)

- Vincent Vatter
- Combinatorics, Probability & Computing
- 2008

Zeilbergerâ€™s enumeration schemes can be used to completely automate the enumeration of many permutation classes. We extend his enumeration schemes so that they apply to many more permutation classesâ€¦ (More)

- Vincent Vatter, Steve Waton
- Order
- 2011

The permutation Ï€ of [n] = {1, 2, . . . , n} contains the permutation Ïƒ of [k] = {1, 2, . . . , k} (written Ïƒ â‰¤ Ï€) if Ï€ has a subsequence of length k order isomorphic to Ïƒ. For example, Ï€ = 391867452â€¦ (More)

- Robert Brignall, Nikola Ruskuc, Vincent Vatter
- Theor. Comput. Sci.
- 2008

Simple permutations are the building blocks of permutation classes. As such, classes with only finitely many simple permutations, e.g., the class of 132-avoiding permutations, have nice properties.â€¦ (More)

- Vincent Vatter
- 2007

We establish a phase transition for permutation classes (downsets of permutations under the permutation containment order): there is an algebraic number Îº, approximately 2.20557, for which there areâ€¦ (More)

- Vincent Vatter
- J. Symb. Comput.
- 2006

Generating trees are a useful technique in the enumeration of various combinatorial objects, particularly restricted permutations. Quite often, the generating tree for the set of permutationsâ€¦ (More)

We determine the MÃ¶bius function of a poset of compositions of an integer. In fact we give two proofs of this formula, one using an involution and one involving discrete Morse theory. Thisâ€¦ (More)

- Robert Brignall, Sophie Huczynska, Vincent Vatter
- J. Comb. Theory, Ser. A
- 2008

A simple permutation is one that does not map a nontrivial interval onto an interval. It was recently proved by Albert and Atkinson that a permutation class with only finitely simple permutations hasâ€¦ (More)

- ABOVE, Vincent Vatter
- 2009

We prove that there are permutation classes (hereditary properties of permutations) of every growth rate (Stanley-Wilf limit) at least Î» 2.48187, the unique real root of x 5 Â¡2x 4 Â¡2x 2 Â¡2xÂ¡1,â€¦ (More)