کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8903681 | 1632911 | 2019 | 42 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On some actions of the 0-Hecke monoids of affine symmetric groups
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات گسسته و ترکیبات
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
There are left and right actions of the 0-Hecke monoid of the affine symmetric group SËn on involutions whose cycles are labelled periodically by nonnegative integers. Using these actions we construct two bijections, which are length-preserving in an appropriate sense, from the set of involutions in SËn to the set of N-weighted matchings in the n-element cycle graph. As an application, we compute a formula for the bivariate generating function counting the involutions in SËn by length and absolute length. The 0-Hecke monoid of SËn also acts on involutions (without any cycle labelling) by Demazure conjugation. The atoms of an involution zâSËn are the minimal length permutations w which transform the identity to z under this action. We prove that the set of atoms for an involution in SËn is naturally a bounded, graded poset, and give a formula for the set's minimum and maximum elements. Using these properties, we classify the covering relations in the Bruhat order restricted to involutions in SËn.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Combinatorial Theory, Series A - Volume 161, January 2019, Pages 178-219
Journal: Journal of Combinatorial Theory, Series A - Volume 161, January 2019, Pages 178-219
نویسندگان
Eric Marberg,