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Questions related to permutations, bijections from a finite (or sometimes infinite) set to itself.

106 votes
Accepted

Conceptual reason why the sign of a permutation is well-defined?

(This is a variant of Cartier's argument mentioned by Dan Ramras.) Let $X$ be a finite set of size at least $2$. Let $E$ be the set of edges of the complete graph on $X$. The set $D$ of ways of dire …
Bjorn Poonen's user avatar
  • 23.8k
6 votes
Accepted

Explicit expression of an alternating polynomial in characteristic $2$?

(Here is a more detailed version of Felipe's answer.) In 1976 Elwyn Berlekamp defined characteristic 2 analogues of the discriminant and its square root, related to the expressions you wrote down. L …
Bjorn Poonen's user avatar
  • 23.8k