It turns out that the set of cyclic orders of [n] becomes a graded poset of length $latex \binom{n}{3}$ under this operation, with unique minimal element $latex n(n-1) \cdots 21$ and unique maximal element $latex 12\cdots (n-1)n$. See https://arxiv.org/abs/0909.5324 for a more general statement related to an arbitrary affine Coxeter group, and see 2010 USAMO Problem 2 for a fun restatement.

Let me know if this seems inteeresting/useful to you!

]]>Anyway, let me know if it seems interesting!

]]>My point is only that it’s a stupid acronym that doesn’t reflect what all of us actually teach. That is my only point and has always been my only point in this post.

I am a Ph.D. in mathematics from UC Berkeley. I am now a full professor in mathematics. I am not making careless errors in calculations. I am questioning the use of an acronym when I think a different acronym or tool may be more clear. Once again, please refrain from including ad hominem attacks in your comments.

]]>(2*3)÷5-6+5

(5÷5)-6+5

(1-6)+5

-5+5

0 ]]>

This is a consequence of Athanasiadis’ formula for going from the F-basis to p-basis (if the function is symmetric!)

https://www.math.upenn.edu/~peal/polynomials/gessel.htm#gesselPowerSum