The power set and the set of permutations with finitely many non‐fixed points of a set

Abstract

AbstractFor a cardinal , we write for the cardinality of the set of permutations with finitely many non‐fixed points of a set which is of cardinality . We investigate the relationships between and for an arbitrary infinite cardinal  in  (without the axiom of choice). It is proved in  that for all infinite cardinals , and we show that this is the best possible result.