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Corpus ID: 226282402

The algebra of binary trees is affine complete

@article{Arnold2021TheAO,
title={The algebra of binary trees is affine complete},
author={Andr{\'e} Arnold and Patrick C{\'e}gielski and Serge Grigorieff and Ir{\`e}ne Guessarian},
journal={Discret. Math. Theor. Comput. Sci.},
year={2021},
volume={23}
}

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.

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 full binary trees whose… Expand

This class of functions from natural integers to integers: those which have integral difference ratios, i.e. verifying f(a) - f(b) ≡ 0 (mod (a - b)) for all a > b is characterized via their representations as Newton series.Expand

Abstract.This paper is a continuation of the research motivated by G. Grätzer’s study of affine completeness for Boolean algebras and distributive lattices from 1962 and 1964, respectively and by the… Expand