Rank Function

Some articles on rank, rank function, ranks:

Graded Poset - Alternative Characterizations
... maximal chains in P have the same length setting the rank of the least element to 0 then determines the rank function completely ... A candidate rank function, compatible with the ordering, makes a poset into graded poset if and only if, whenever one has x < z with z of rank n+1, an element y of ... of x, the only possible choice is y = x showing that the ranks of x and z differ by 1, and it is necessary because in a graded poset one can take for y any element of maximal rank with x ≤ y < z ...

Famous quotes containing the words function and/or rank:

    It is not the function of our Government to keep the citizen from falling into error; it is the function of the citizen to keep the Government from falling into error.
    Robert H. [Houghwout] Jackson (1892–1954)

    If we were left solely to the wordy wit of legislators in Congress for our guidance, uncorrected by the seasonable experience and the effectual complaints of the people, America would not long retain her rank among the nations.
    Henry David Thoreau (1817–1862)