Cycle notation for cyclic orders Is there a convenient cycle notation for cyclic orders (https://en.wikipedia.org/wiki/Cyclic_order)?
For example:
Definition. A set of four elements $a, b, c, d$ of a cyclically ordered set is a 4-cycle $[a, b, c, d]$ if $[a,b,c] \land [c,d,a]$.
Using transitivity it is easy to show that
$[a, b, c, d] \implies [a,b,c]$, $[b,c,d]$, $[c,d,a]$, $[d,a,b]$, and all the cyclic equivalents:
$[b,c,a]$, $[c,a,b]$, $[c,d,b]$, $[d,b,c]$, $[a,c,d]$, $[d,a,c]$, $[a,b,d]$, $[b,d,a]$.
Which also means $[a, b, c, d] \iff [b, c, d, a] \iff [c, d, a, b] \iff [d, a, b, c]$.
It could simplify the ternary arithmetic.

I am not aware of any standard notation, but your notation $[a, b, c, d]$ makes sense and could be extended to $[a_1, a_2, \dotsm, a_n]$ for any $n$.
