کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
420222 683907 2011 7 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A new Euler–Mahonian constructive bijection
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نظریه محاسباتی و ریاضیات
پیش نمایش صفحه اول مقاله
A new Euler–Mahonian constructive bijection
چکیده انگلیسی

Using generating functions, MacMahon proved in 1916 the remarkable fact that the major index has the same distribution as the inversion number for multiset permutations, and in 1968 Foata gave a constructive bijection proving MacMahon’s result. Since then, many refinements have been derived, consisting of adding new constraints or new statistics.Here we give a new simple constructive bijection between the set of permutations with a given number of inversions and those with a given major index. We introduce a new statistic, mix, related to the Lehmer code, and using our new bijection we show that the bistatistic (mix,INV) is Euler–Mahonian. Finally, we introduce the McMahon code for permutations which is the major-index counterpart of the Lehmer code and show that the two codes are related by a simple relation.


► We give a simple bijection between permutations with a given number of inversions and a given major index.
► A new statistic, mix, is introduced.
► We show that the bistatistic (mix,INV) is Euler–Mahonian.
► We introduce a McMahon code for permutations.
► This code is simply related to the Lehmer code.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Discrete Applied Mathematics - Volume 159, Issue 14, 28 August 2011, Pages 1453–1459
نویسندگان
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