Generating countable sets of surjective functions

• Autorzy: J. D. Mitchell , Y. Péresse
• Języki publikacji: EN

Abstrakty

EN

We prove that any countable set of surjective functions on an infinite set of cardinality ℵₙ with n ∈ ℕ can be generated by at most n²/2 + 9n/2 + 7 surjective functions of the same set; and there exist n²/2 + 9n/2 + 7 surjective functions that cannot be generated by any smaller number of surjections. We also present several analogous results for other classical infinite transformation semigroups such as the injective functions, the Baer-Levi semigroups, and the Schützenberger monoids.

Kategorie tematyczne

• 20M20: Semigroups of transformations, etc.
• 03E05: Other combinatorial set theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2011
• Tom: 213
• Numer: 1
• Strony: 67-93

Daty

wydano

2011

Twórcy

autor

J. D. Mitchell

• Mathematical Institute, North Haugh, St Andrews, Fife, KY16 9SS, Scotland

autor

Y. Péresse

• Mathematical Institute, North Haugh, St Andrews, Fife, KY16 9SS, Scotland

Identyfikatory

DOI

10.4064/fm213-1-4