Suppose $X,Y$ are two subsets of order $n$. Consider the set of all one to one and onto functions $f$ such that $f(X)=X$ and $f(Y)=Y$. Then it is an easy problem that automorphism group of all these functions is $S_n\times S_n$. Now, what is the automorphism group of all one to one and onto functions such that $f(X)=X, f(Y)=Y$ or $f(X)=Y, f(Y)=X$?
2026-04-22 14:40:16.1776868816
Automorphism group of a some kind of functions
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