2017 USAMO Problems/Problem 2
Revision as of 18:48, 21 November 2018 by Scrabbler94 (talk | contribs) (→Problem: added full text of problem)
Problem
Let be a collection of
positive integers, not necessarily distinct. For any sequence of integers
and any permutation
of
, define an
-inversion of
to be a pair of entries
with
for which one of the following conditions holds:
or
Show that, for any two sequences of integers
and
, and for any positive integer
, the number of permutations of
having exactly
-inversions is equal to the number of permutations of
having exactly
-inversions.