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László Zádori: Connnectivity in the digraph of polynomials (in Hungarian)

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Wednesday, 23. April 2014, 10:00 - 12:00
Abstract: With every digraph we associate an algebra whose fundamental operations are the polymorphisms of the digraph. A digraph is smooth, if it has no sinks and no sources. Smooth digraphs of algebraic length 1 are a broad generalization  of reflexive digraphs. In the present talk we sketch a proof that the digraph of unary polynomial operations of the algebra associated with a finite connected smooth digraph of algebraic length 1 is connected, provided that the algebra lies in a congruence join-semidistributive over modular variety. This generalizes our earlier connectivity result obtained for reflexive digraphs and implies the restricted version of the famous Loop Lemma of Barto et al. in the congruence join-semidistributive over modular case.  In the proofs we make a good use of the twin relation introduced by E. W. Kiss. The new results in the talk were obtained in a joint work with G. Gyenizse and M. Maróti.
Location : Bolyai Intézet, I. Kórház, fszt. 17., folyóirat-olvasó terem

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