A Discontinuity in the Distribution of Fixed Point Sums

Edward A. Bender, E. Rodney Canfield, L. Bruce Richmond +1

The quantity $f(n,r)$, defined as the number of permutations of the set $[n]=\{1,2,...n\}$ whose fixed points sum to $r$, shows a sharp discontinuity in the neighborhood of $r=n$.…