کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
10118341 1632851 2005 10 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Refined sign-balance on 321-avoiding permutations
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات گسسته و ترکیبات
پیش نمایش صفحه اول مقاله
Refined sign-balance on 321-avoiding permutations
چکیده انگلیسی
The number of even 321-avoiding permutations of length n is equal to the number of odd ones if n is even, and exceeds it by the n−12th Catalan number otherwise. We present an involution that proves a refinement of this sign-balance property respecting the length of the longest increasing subsequence of the permutation. In addition, this yields a combinatorial proof of a recent analogous result of Adin and Roichman dealing with the last descent. In particular, we answer the question of how to obtain the sign of a 321-avoiding permutation from the pair of tableaux resulting from the Robinson-Schensted-Knuth algorithm. The proof of the simple solution is based on a matching method given by Elizalde and Pak.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: European Journal of Combinatorics - Volume 26, Issue 6, August 2005, Pages 1009-1018
نویسندگان
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