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