SMOOTH SQUARED, TRIANGULAR, AND HEXAGONAL BARGRAPHS

Toufik Mansour

doi:10.2298/AADM220603003M

SMOOTH SQUARED, TRIANGULAR, AND HEXAGONAL BARGRAPHS

Toufik Mansour

Department of Mathematics

University of Haifa

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we find an explicit formula for the generating function for the number of smooth squared (triangular, hexagonal) bargraphs according to the perimeter and number of columns. In particular, we show that the number of smooth squared, triangular, and hexagonal bargraphs with perimeter 2n (resp. n, 2n) is asymptotic to (Formula presented.), where (Formula presented.), r_t is the smallest positive root of the polynomial p¹⁶−2p¹⁴+p¹²−2p¹¹−2p¹⁰+2p⁹+4p⁸−5p⁶−2p⁵+p⁴−2p³−2p²+1 and c_s, c_t, c_h are three constants, as n ↦ ∞.

Original language	American English
Pages (from-to)	215-228
Number of pages	14
Journal	Applicable Analysis and Discrete Mathematics
Volume	18
Issue number	1
DOIs	https://doi.org/10.2298/AADM220603003M
State	Published - 2024

Keywords

Bargraphs
Hexagonal bargraphs
Smooth bargraphs
Squared bargraphs
Triangular bargraphs

All Science Journal Classification (ASJC) codes

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

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10.2298/AADM220603003M

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AB - In this paper, we find an explicit formula for the generating function for the number of smooth squared (triangular, hexagonal) bargraphs according to the perimeter and number of columns. In particular, we show that the number of smooth squared, triangular, and hexagonal bargraphs with perimeter 2n (resp. n, 2n) is asymptotic to (Formula presented.), where (Formula presented.), rt is the smallest positive root of the polynomial p16−2p14+p12−2p11−2p10+2p9+4p8−5p6−2p5+p4−2p3−2p2+1 and cs, ct, ch are three constants, as n ↦ ∞.

KW - Bargraphs

KW - Hexagonal bargraphs

KW - Smooth bargraphs

KW - Squared bargraphs

KW - Triangular bargraphs

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DO - 10.2298/AADM220603003M

M3 - Article

SN - 1452-8630

VL - 18

SP - 215

EP - 228

JO - Applicable Analysis and Discrete Mathematics

JF - Applicable Analysis and Discrete Mathematics

IS - 1

ER -

SMOOTH SQUARED, TRIANGULAR, AND HEXAGONAL BARGRAPHS

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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