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Év szerint | Hónap szerint | Ugrás a hónaphoz | |
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Ádám Kunos: Słupecki digraphs |
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Szerda, 15. Február 2023, 10:10 - 11:40
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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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