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A monoid version of the Brin-Higman-Thompson groups
We generalize the Brin-Higman-Thompson groups to monoids , for and , by replacing bijections by partial
functions. The monoid has as its group of units, and is
congruence-simple. Moreover, is finitely generated, and for its word problem is {\sf coNP}-complete. We also present new results about
higher-dimensional joinless codes.Comment: 26 page