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- W2148713750 abstract "The quantity $f(n,r)$, defined as the number of permutations of the set $[n]={1,2,dots n}$ 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." @default.
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- W2148713750 date "2003-04-23" @default.
- W2148713750 modified "2023-09-30" @default.
- W2148713750 title "A Discontinuity in the Distribution of Fixed Point Sums" @default.
- W2148713750 cites W2047572897 @default.
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- W2148713750 doi "https://doi.org/10.37236/1708" @default.
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