0

Recall that writing a function $f\in S_4$ in disjoint cycle form amounts to writing it as

$f=(1,4)(2,3)$, for example. If, for instance $4$ is a fixed point. That is, $f(4)=4$, and we have $f(1)=2, f(2)=3, f(3)=1$, then we write $f=(1,2,3)$.

How do we notate a function that is only fixed points? For example $f(x)=x, \forall x\in${$1,2,3,4$}.

  • For the identity in $S_n$ we write sometimes $(1)$. – Dietrich Burde Oct 29 '16 at 18:10
  • Also here at MSE this seems to be standard. So $S_4$ is written out as $$ S_4={(1), (12), (13), (14), (23), (24), (34), (123), (132), (142), (124), (134), (143), (234), (243), (1234), (1243), (1324), (1342), (1423), (1432), (12)(34), (13)(24), (14)(23)} $$, see here. – Dietrich Burde Oct 29 '16 at 18:38

0 Answers0