کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4949693 1440202 2017 13 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Statistics on bargraphs viewed as cornerless Motzkin paths
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نظریه محاسباتی و ریاضیات
پیش نمایش صفحه اول مقاله
Statistics on bargraphs viewed as cornerless Motzkin paths
چکیده انگلیسی
A bargraph is a self-avoiding lattice path with steps U=(0,1), H=(1,0) and D=(0,−1) that starts at the origin and ends on the x-axis, and stays strictly above the x-axis everywhere except at the endpoints. Bargraphs have been studied as a special class of convex polyominoes, and enumerated using the so-called wasp-waist decomposition of Bousquet-Mélou and Rechnitzer. In this paper we note that there is a trivial bijection between bargraphs and Motzkin paths without peaks or valleys. This allows us to use the recursive structure of Motzkin paths to enumerate bargraphs with respect to several statistics, finding simpler derivations of known results and obtaining many new ones. We also count symmetric bargraphs and alternating bargraphs. In some cases we construct statistic-preserving bijections between different combinatorial objects, proving some identities that we encounter along the way.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Discrete Applied Mathematics - Volume 221, 20 April 2017, Pages 54-66
نویسندگان
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