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On the length of word chains. (English) Zbl 0654.68096

Word chains are an extension of addition chains to words. We show that over a q-letter alphabet, any long enough word admits a word chain of length at most \((1+\epsilon)n/\log_ q n\), for a fixed arbitrary \(\epsilon >0\); there exist words with no chain shorter than \(n/\log_{q- 1} n\). Several examples are given. Finally, we show that words with few factors have short chains.

MSC:

68Q45 Formal languages and automata
68Q42 Grammars and rewriting systems
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