There is the algebraic expression a+b+c. If we replace under the rule {a->b, b->c, c->a}, the expression is left unchanged. But for expressions like 2a+b+c, the replacement will change the expression. What is the word to describe this kind of symmetry? Thanks

  • Is there any term in English? Or you are looking for an algebraic jargon?
    – Maulik V
    Mar 15, 2014 at 12:35
  • 1
    I suggest that this asks for a term of art and belongs on Mathematics. Mar 15, 2014 at 14:16
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    If f(x,y,z) = f(y,z,x), then f(x,y,z) is a cyclic expression. Mar 15, 2014 at 17:03
  • @DamkerngT. - I think you should make that an answer, because I think that is the answer.
    – J.R.
    Mar 15, 2014 at 20:28
  • @StoneyB - I just checked the help pages at the Mathematics, and I don't think this question would be a good fit for their site. It doesn't seem like it would be on-topic there.
    – J.R.
    Mar 15, 2014 at 20:30

1 Answer 1


The term for it is Cyclic Expressions.

I just found a good page that explains Symmetric and Cyclic Expressions. According to the page,

An expression f(x,y,z) is said to be a cyclic expression if f(x,y,z) = f(y,z,x).

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