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2r+l abelian group adjacency matrix algebraic algorithm associative closure atomic formulas automorphism automorphism group axioms Banach space Billigheimer binary blocks braid chromatic polynomial clauses column contains corresponding defined denote derivatives Desargues configurations differentiable edge eigenvalues elements entries equations equivalent exists finite formula function given graph groupoid Hence hexads IDEMPOTENT implies incident integer interactive method irreducible isomorphic job table Laguerre plane Lemma lex characters lexical instances lexical system lexical table lexical terms linear Math mathematical matrix Moebius Moebius plane notation operator pairs permutation planar maps points polynomial problem proof procedure proof set prove RABECGI result rooted rough norm self-adjoint semigroup sequence SETTIME solution spline strand structure subset theorem theory topological University of Manitoba vector vertex vertices W. T. Tutte zero