Avoiding Three Consecutive Blocks of the Same Size and Same Sum

2011/06/26 by Cassaigne, Julien, Currie, James D., Schaeffer, Luke +1 · 2 citations
#Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics

paper · doi:10.48550/arxiv.1106.5204

Abstract

We show that there exists an infinite word over the alphabet 0, 1, 3, 4 containing no three consecutive blocks of the same size and the same sum. This answers an open problem of Pirillo and Varricchio from 1994.

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• Words with factor complexity 2n+1 and minimal critical exponent
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