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 (1922–1986)
“Motherhood in all its guises and permutations is more art than science.”
—Melinda M. Marshall (20th century)
“In the end we beat them with Levi 501 jeans. Seventy-two years of Communist indoctrination and propaganda was drowned out by a three-ounce Sony Walkman. A huge totalitarian system ... has been brought to its knees because nobody wants to wear Bulgarian shoes.... Now they’re lunch, and we’re number one on the planet.”
—P.J. (Patrick Jake)
“Words can have no single fixed meaning. Like wayward electrons, they can spin away from their initial orbit and enter a wider magnetic field. No one owns them or has a proprietary right to dictate how they will be used.”
—David Lehman (b. 1948)
“There are good points about all such wars. People forget self. The virtues of magnanimity, courage, patriotism, etc., etc., are called into life. People are more generous, more sympathetic, better, than when engaged in the more selfish pursuits of peace.”
—Rutherford Birchard Hayes (1822–1893)