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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
In this paper, we study the number of bargraphs with $n$ cells and $m$ columns according to the distribution for the statistic that records the number of times a given shape lies entirely within a bargraph for various small shapes.
📌 3 Key Takeaways
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Objective & Hypothesis:Bargraphs are lattice paths in $\mathbb{N}_0^2$ that start at the origin and end upon their first return to the $x$-axis.
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Key Findings & Data:Each bargraph is represented by a sequence of column heights $\pi_1\pi_2\cdots\pi_m$ such that column $j$ contains $\pi_j$ cells.
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Conclusion & Impact:In this paper, we study the number of bargraphs with $n$ cells and $m$ columns according to the distribution for the statistic that records the number of times a given shape lies entirely within a bargraph for various small shapes.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Bargraphs · generating functions · $C$-vertices
Abstract
Bargraphs are lattice paths in $\mathbb{N}_0^2$ that start at the origin and end upon their first return to the $x$-axis. Each bargraph is represented by a sequence of column heights $\pi_1\pi_2\cdots\pi_m$ such that column $j$ contains $\pi_j$ cells. In this paper, we study the number of bargraphs with $n$ cells and $m$ columns according to the distribution for the statistic that records the number of times a given shape lies entirely within a bargraph for various small shapes.
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Cite This Article
MANSOUR, T., SHABANI, A. (2018). Bargraphs in bargraphs. Turkish Journal of Mathematics, Cilt: 42 - Sayı: 5, 2763–2773. https://ajindex.com/articles/723078