Cycles and Fixed Points - Counting Permutations By Number of Cycles

Counting Permutations By Number of Cycles

The unsigned Stirling number of the first kind, s(k, j) counts the number of permutations of k elements with exactly j disjoint cycles.

Read more about this topic:  Cycles And Fixed Points

Famous quotes containing the words counting, permutations, number and/or cycles:

    What we commonly call man, the eating, drinking, planting, counting man, does not, as we know him, represent himself, but misrepresents himself. Him we do not respect, but the soul, whose organ he is, would he let it appear through his action, would make our knees bend.
    Ralph Waldo Emerson (1803–1882)

    Motherhood in all its guises and permutations is more art than science.
    Melinda M. Marshall (20th century)

    While I do not suggest that humanity will ever be able to dispense with its martyrs, I cannot avoid the suspicion that with a little more thought and a little less belief their number may be substantially reduced.
    —J.B.S. (John Burdon Sanderson)

    The stars which shone over Babylon and the stable in Bethlehem still shine as brightly over the Empire State Building and your front yard today. They perform their cycles with the same mathematical precision, and they will continue to affect each thing on earth, including man, as long as the earth exists.
    Linda Goodman (b. 1929)