Notation for symmetric closure of a relation

Question

Given a binary relation $r$, its reflexive closure, $r \cup id$, is sometimes written as $r^?$ or $r^=$. Its transitive closure is written as $r^+$. Its reflexive, transitive closure is written as $r^*$.

What about its symmetric closure, $r \cup r^{-1}$? Is there any existing notation for that? I saw $s(r)$ once, but that's not particularly appealing to me. Are there any other candidates?

Answer 1

I would use $R^s$ for the symmetrisation of a relation $R$, as in this link.

By symmetrization of the binary relation $R$ on a set one obtains the symmetric relation $R^s$ defined by: $a \mathrel{R^s} b$ if and only if $a \mathrel{R} b$ or $b \mathrel{R} a$, such that every symmetric relation implying $\mathrel{R}$ also implies $\mathrel{R^s}$.

Zassenhaus, Hans J. The theory of groups. 2nd ed. Chelsea Publishing Company, New York, 1958. 265 pp.