A Discontinuity in the Distribution of Fixed Point Sums
| dc.creator | Bender, Edward A. | |
| dc.creator | Canfield, E. Rodney | |
| dc.creator | Richmond, L. Bruce | |
| dc.creator | Wilf, Herbert S. | |
| dc.date | 2003-04-25 | |
| dc.date.accessioned | 2026-07-07T04:57:25Z | |
| dc.date.available | 2026-07-07T04:57:25Z | |
| dc.description | 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 $r=n$. We explain this discontinuity and study the possible existence of other discontinuities in $f(n,r)$ for permutations. We generalize our results to other families of structures that exhibit the same kind of discontinuities, by studying $f(n,r)$ when ``fixed points'' is replaced by ``components of size 1'' in a suitable graph of the structure. Among the objects considered are permutations, all functions and set partitions. | |
| dc.description | 1 figure | |
| dc.identifier | https://arxiv.org/abs/math/0304416 | |
| dc.identifier | http://arxiv.org/abs/math/0304416 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67258 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A17, 05A20 | |
| dc.title | A Discontinuity in the Distribution of Fixed Point Sums | |
| dc.type | text |