کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6872100 | 681607 | 2015 | 10 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Enumerations of humps and peaks in (k,a)-paths and (n,m)-Dyck paths via bijective proofs
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موضوعات مرتبط
مهندسی و علوم پایه
مهندسی کامپیوتر
نظریه محاسباتی و ریاضیات
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Enumerations of humps and peaks in (k,a)-paths and (n,m)-Dyck paths via bijective proofs Enumerations of humps and peaks in (k,a)-paths and (n,m)-Dyck paths via bijective proofs](/preview/png/6872100.png)
چکیده انگلیسی
Recently Mansour and Shattuck studied (k,a)-paths and gave formulas that related the total number of humps in all (k,a)-paths to the number of super (k,a)-paths. These results generalized earlier results of Regev on Dyck paths and Motzkin paths. Their proofs are based on generating functions and they asked for bijective proofs for their results. In this paper we first give bijective proofs of Mansour and Shattuck's results, then we extend our study to (n,m)-Dyck paths. We give a bijection that relates the total number of peaks in all (n,m)-Dyck paths to certain free (n,m)-paths when n and m are coprime. From this bijection we get the number of (n,m)-Dyck paths with exactly j peaks, which is a generalization of the well-known result that the number Dyck paths of order n with exactly j peaks is the Narayana number 1knâ1kâ1nkâ1.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Discrete Applied Mathematics - Volumes 190â191, 20 August 2015, Pages 42-49
Journal: Discrete Applied Mathematics - Volumes 190â191, 20 August 2015, Pages 42-49
نویسندگان
Rosena R.X. Du, Yingying Nie, Xuezhi Sun,