Composition of axial functions of products of finite sets

Krzysztof Płotka. "Composition of axial functions of products of finite sets." Colloquium Mathematicae 107.1 (2007): 15-20. <http://eudml.org/doc/284070>.

@article{KrzysztofPłotka2007,
abstract = {We show that every function f: A × B → A × B, where |A| ≤ 3 and |B| < ω, can be represented as a composition f₁ ∘ f₂ ∘ f₃ ∘ f₄ of four axial functions, where f₁ is a vertical function. We also prove that for every finite set A of cardinality at least 3, there exist a finite set B and a function f: A × B → A × B such that f ≠ f₁ ∘ f₂ ∘ f₃ ∘ f₄ for any axial functions f₁, f₂, f₃, f₄, whenever f₁ is a horizontal function.},
author = {Krzysztof Płotka},
journal = {Colloquium Mathematicae},
keywords = {axial functions},
language = {eng},
number = {1},
pages = {15-20},
title = {Composition of axial functions of products of finite sets},
url = {http://eudml.org/doc/284070},
volume = {107},
year = {2007},
}

TY - JOUR
AU - Krzysztof Płotka
TI - Composition of axial functions of products of finite sets
JO - Colloquium Mathematicae
PY - 2007
VL - 107
IS - 1
SP - 15
EP - 20
AB - We show that every function f: A × B → A × B, where |A| ≤ 3 and |B| < ω, can be represented as a composition f₁ ∘ f₂ ∘ f₃ ∘ f₄ of four axial functions, where f₁ is a vertical function. We also prove that for every finite set A of cardinality at least 3, there exist a finite set B and a function f: A × B → A × B such that f ≠ f₁ ∘ f₂ ∘ f₃ ∘ f₄ for any axial functions f₁, f₂, f₃, f₄, whenever f₁ is a horizontal function.
LA - eng
KW - axial functions
UR - http://eudml.org/doc/284070
ER -