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On divided-difference semigroups
journal contributionposted on 2023-05-26, 10:24 authored by FitzGerald, DG
The Newtonian divided-di¬¨¬ßerence operators generate the nil-Coxeter algebra and semigroup. A bijective correspondence between the nil-Coxeter semigroup and the symmetric group is used to provide braid-like diagrams for the former, and corresponding Reidemeister-type moves for the relations. Conditions are given for similar relations to hold in a skew group ring. Interesting extensions of the nil-Coxeter semigroup are described and given diagrammatic representations.
Publication titleInternational Journal of Algebra and Computation
Rights statementAuthor version dated December 21, 2009--Preprint of an article submitted for consideration in International Journal of Algebra and Computation Copyright 2009 World Scientific Publishing Company