Affiliation:
1. Department of Mathematics, University of Haifa, Haifa, Israel
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 csr1?ns/??n3 (resp. ctr1?nt/??n3, ch/??n3?2n+2 ), where rs = 1+ 3?181+24?78/12 ? 23/12 3?181+24?78, 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 are two
constants, as n ? ?.
Publisher
National Library of Serbia
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