کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4651872 | 1632582 | 2015 | 8 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
The Bruhat order on conjugation-invariant sets of involutions in the symmetric group
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات گسسته و ترکیبات
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
Let InIn be the set of involutions in the symmetric group SnSn, and for A⊆{0,1,...,n}A⊆{0,1,...,n}, letFnA={σ∈In|σ has a fixed points for some a∈A}. We give a complete characterisation of the sets A for which FnA, with the order induced by the Bruhat order on SnSn, is a graded poset. In particular, we prove that Fn{1} (i.e., the set of involutions with exactly one fixed point) is graded, which settles a conjecture of Hultman in the affirmative. When FnA is graded, we give its rank function. We also give a short new proof of the EL-shellability of Fn{0} (i.e., the set of fixed point-free involutions), which was recently proved by Can, Cherniavsky, and Twelbeck.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Electronic Notes in Discrete Mathematics - Volume 49, November 2015, Pages 3–10
Journal: Electronic Notes in Discrete Mathematics - Volume 49, November 2015, Pages 3–10
نویسندگان
Mikael Hansson,