Some combinatorial results on smooth permutations

Shoni Gilboa, Erez Lapid

نتاج البحث: نشر في مجلةمقالةمراجعة النظراء


We show that any smooth permutation w is characterized by the set C(w) of transpositions and 3-cycles that are ≤ w in the Bruhat order and that w is the product (in a certain order) of the transpositions in C(w). We also characterize the image of the map w 7! C(w). This map is closely related to the essential set (in the sense of Fulton) and gives another approach for enumerating smooth permutations and subclasses thereof. As an application, we obtain a result about the intersection of the Bruhat interval defined by a smooth permutation with a conjugate of a parabolic subgroup of the symmetric group. Finally, we relate covexillary permutations to smooth ones.

اللغة الأصليةالإنجليزيّة
رقم المقال81
دوريةSeminaire Lotharingien de Combinatoire
رقم الإصدار84
حالة النشرنُشِر - 2020

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