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:
“Love is sinister,
is mean to us in separation;
makes our thin bodies thinner.
This fellow Death
lacks mercy
and is good at counting our days.
And Master,
you, too, are subject
to the plague of jealousy
so think:
how could womenfolk,
soft as sprouts,
live like this?”
—Amaru (c. seventh century A.D.)
“Motherhood in all its guises and permutations is more art than science.”
—Melinda M. Marshall (20th century)
“After a certain number of years our faces become our biographies. We get to be responsible for our faces.”
—Cynthia Ozick (b. 1928)
“It is not merely the likeness which is precious ... but the association and the sense of nearness involved in the thing ... the fact of the very shadow of the person lying there fixed forever! It is the very sanctification of portraits I thinkand it is not at all monstrous in me to say ... that I would rather have such a memorial of one I dearly loved, than the noblest Artists work ever produced.”
—Elizabeth Barrett Browning (18061861)
“In writing biography, fact and fiction shouldnt be mixed. And if they are, the fictional points should be printed in red ink, the facts printed in black ink.”
—Catherine Drinker Bowen (18971973)