On column-convex and convex Carlitz polyominoes

2021/01/31 by Toufik, Mansour, Rastegar, Reza, Shabani, Armend
#05A16 #05B50 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2102.00445

Abstract

In this paper, we introduce and study \it Carlitz polyominoes. In particular, we show that, as n grows to infinity, asymptotically the number of \beginenumerate \item column-convex Carlitz polyominoes with perimeter 2n is \beq (9√(2)(14+3√(3)))/(2704√(πn³))4ⁿ. \feq \item convex Carlitz polyominoes with perimeter 2n is \beq (n+1)/(10)((3+√(5))/(2))^n-2. \feq \endenumerate

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