Counting Permutations By Number of Fixed Points
The value f(k, j) counts the number of permutations of k elements with exactly j fixed points. For the main article on this topic, see rencontres numbers.
Read more about this topic: Cycles And Fixed Points
Famous quotes containing the words counting, permutations, number, fixed and/or points:
“But counting up to two
Is harder to do....”
—Philip Larkin (19221986)
“The new shopping malls make possible the synthesis of all consumer activities, not least of which are shopping, flirting with objects, idle wandering, and all the permutations of these.”
—Jean Baudrillard (b. 1929)
“This nightmare occupied some ten pages of manuscript and wound off with a sermon so destructive of all hope to non-Presbyterians that it took the first prize. This composition was considered to be the very finest effort of the evening.... It may be remarked, in passing, that the number of compositions in which the word beauteous was over-fondled, and human experience referred to as lifes page, was up to the usual average.”
—Mark Twain [Samuel Langhorne Clemens] (18351910)
“...stare into the lake of sunset as it runs
boiling, over the west past all control
rolling and swamps the heartbeat and repeats
sea beyond sea after unbearable suns;
think: poems fixed this landscape: Blake, Donne, Keats.”
—Muriel Rukeyser (19131980)
“Every man has to learn the points of the compass again as often as he awakes, whether from sleep or any abstraction.”
—Henry David Thoreau (18171862)