2025/02/28 by Ochem, Pascal, Pierron, Théo
#Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics
paper · doi:10.48550/arxiv.2502.20774
A tangram is a word in which every letter occurs an even number of times. Thus it can be cut into parts that can be arranged into two identical words. The cut number of a tangram is the minimum number of required cuts in this process. Tangrams with cut number one corresponds to squares. For k≥1, let t(k) denote the minimum size of an alphabet over which an infinite word avoids tangrams with cut number at most~k. The existence of infinite ternary square-free words shows that t(1)=t(2)=3. We show that t(3)=t(4)=4, answering a question from Dębski, Grytczuk, Pawlik, Przybyło, and Śleszyńska-Nowak.