Decision problems for inverse monoids presented by a single sparse relator |
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Authors: | Susan Hermiller Steven Lindblad John Meakin |
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Affiliation: | 1. Department of Mathematics, University of Nebraska, Lincoln, NE, 68588-0130, USA 2. Hewitt Associates LLC, 45 South 7th Street, Suite 2100, Minneapolis, MN, 55402, USA
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Abstract: | We study a class of inverse monoids of the form M=Inv 〈X∣w=1〉, where the single relator w has a combinatorial property that we call sparse. For a sparse word w, we prove that the word problem for M is decidable. We also show that the set of words in (X∪X −1)* that represent the identity in M is a deterministic context free language, and that the set of geodesics in the Schützenberger graph of the identity of M is a regular language. |
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