Cycles and Fixed Points - Counting Permutations By Number of Fixed Points

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

“Is it not manifest that our academic institutions should have a wider scope; that they should not be timid and keep the ruts of the last generation, but that wise men thinking for themselves and heartily seeking the good of mankind, and counting the cost of innovation, should dare to arouse the young to a just and heroic life; that the moral nature should be addressed in the school-room, and children should be treated as the high-born candidates of truth and virtue?”
—Ralph Waldo Emerson (1803–1882)

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

“The two great points of difference between a democracy and a republic are: first, the delegation of the government, in the latter, to a small number of citizens elected by the rest; secondly, the greater number of citizens and greater sphere of country over which the latter may be extended.”
—James Madison (1751–1836)

“... social evils are dangerously contagious. The fixed policy of persecution and injustice against a class of women who are weak and defenseless will be necessarily hurtful to the cause of all women.”
—Fannie Barrier Williams (1855–1944)

“The two great points of difference between a democracy and a republic are: first, the delegation of the government, in the latter, to a small number of citizens elected by the rest; secondly, the greater number of citizens and greater sphere of country over which the latter may be extended.”
—James Madison (1751–1836)