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Ádám Kunos: Słupecki digraphs

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Wednesday, 15. February 2023, 10:10 - 11:40
Call a relational structure Słupecki if its surjective polymorphisms
are all essentially unary. It is clear that if a structure has this
property, then its idempotent polymorphisms are projections, i.e. it
is idempotent-trivial. We say that a relational structure is
2-idempotent-trivial if its binary idempotent polymorphisms are
projections. In a 1991 paper, Benoit Larose showed that if a poset
(having at least three elements) is 2-idempotent-trivial, then it is
idempotent-trivial. I joined him and his PhD student, David Emmanuel
Pazmiño, last summer to do some research on Słupecki digraphs, a topic
they had already been investigating for some time. One specific
question of Larose was whether some analogue of his result, mentioned
above, holds for Słupeckiness. We managed to answer this question in
the negative. In this talk, after some review of previous results on
Słupecki digraphs, we show our counterexamples to Larose's question.
Joint work with Benoit Larose and David Emmanuel Pazmiño.

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