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The algebra of binary trees is affine complete

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 04 Nov 2021Embargo end date: 01 Nov 2020 France English Publisher:Centre pour la Communication Scientifique Directe (CCSD)Journal:Discrete Mathematics & Theoretical Computer Science, volume vol. 23 no. 2, special issue... (eissn: 1365-8050, Copyright policy )
Authors: Arnold, André; Cégielski, Patrick; Grigorieff, Serge; Guessarian, Irène;

doi: 10.46298/dmtcs.6890 , 10.48550/arxiv.2011.03925

arXiv: 2011.03925

The algebra of binary trees is affine complete

Abstract

A function on an algebra is congruence preserving if, for any congruence, it maps pairs of congruent elements onto pairs of congruent elements. We show that on the algebra of binary trees whose leaves are labeled by letters of an alphabet containing at least three letters, a function is congruence preserving if and only if it is polynomial.

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Keywords

FOS: Computer and information sciences, Formal Languages and Automata Theory (cs.FL), 06A99, 08A30, 08B20, congruences, Computer Science - Formal Languages and Automata Theory, trees, [MATH] Mathematics [math], 06a99, 08a30, 08b20, algebras, computer science - formal languages and automata theory, QA1-939, Mathematics, [INFO.INFO-FL] Computer Science [cs]/Formal Languages and Automata Theory [cs.FL]

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selected citations
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This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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