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Abstract

The Newtonian divided-di¤erence 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.

Item Type:	Article
Authors/Creators:	FitzGerald, DG
Keywords:	Keywords: divided-di¤erences, nil-Coxeter algebra, Bruhat order, diagram semigroups, presentations.
Journal or Publication Title:	International Journal of Algebra and Computation
ISSN:	0218-1967
DOI / ID Number:	10.1142/S0218196711006121
Additional Information:	Author version dated December 21, 2009--Preprint of an article submitted for consideration in International Journal of Algebra and Computation © 2009 World Scientific Publishing Company <http://ejournals.worldscientific.com.sg/ijac/ijac.shtml>
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