Reduced decompositions and permutation patterns
نویسنده
چکیده
Billey, Jockusch, and Stanley characterized 321-avoiding permutations by a property of their reduced decompositions. This paper generalizes that result with a detailed study of permutations via their reduced decompositions and the notion of pattern containment. These techniques are used to prove a new characterization of vexillary permutations in terms of their principal dual order ideals in a particular poset. Additionally, the combined frameworks yield several new results about the commutation classes of a permutation. In particular, these describe structural aspects of the corresponding graph of the classes and the zonotopal tilings of a polygon defined by Elnitsky that is associated with the permutation.
منابع مشابه
ar X iv : m at h / 05 06 24 2 v 2 [ m at h . C O ] 1 2 Ju l 2 00 5 REDUCED DECOMPOSITIONS AND PERMUTATION PATTERNS
Billey, Jockusch, and Stanley characterized 321-avoiding permutations by a property of their reduced decompositions. This paper generalizes that result with a detailed study of permutations via their reduced decompositions and the notion of pattern containment. These techniques are used to prove a new characterization of vexillary permutations in terms of their principal dual order ideals in a ...
متن کاملar X iv : m at h / 05 06 24 2 v 3 [ m at h . C O ] 1 7 Fe b 20 06 REDUCED DECOMPOSITIONS AND PERMUTATION PATTERNS
Billey, Jockusch, and Stanley characterized 321-avoiding permutations by a property of their reduced decompositions. This paper generalizes that result with a detailed study of permutations via their reduced decompositions and the notion of pattern containment. These techniques are used to prove a new characterization of vexillary permutations in terms of their principal dual order ideals in a ...
متن کاملar X iv : m at h / 05 06 24 2 v 1 [ m at h . C O ] 1 3 Ju n 20 05 REDUCED DECOMPOSITIONS AND PERMUTATION PATTERNS
Billey, Jockusch, and Stanley characterized 321-avoiding permutations by a property of their reduced decompositions. This paper generalizes that result with a detailed study of permutations via their reduced decompositions and the notion of pattern containment. These techniques are used to prove a new characterization of vexillary permutations in terms of their principal dual order ideals in a ...
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