Geodesic
Rankings and Ranking Functions
Canadian journal of mathematics, Tome 33 (1981) no. 2, pp. 395-399

Voir la notice de l'article provenant de la source Cambridge University Press

Suppose that n competitors compete in r races and in each race they are awarded placings l, 2, 3, ..., n – 1, n. After the r races each competitor has a result consisting of his r placings. Let such a result be written (α j )1≦j≦r where for convenience the positive integers α j are arranged in ascending order. For example, if n = 4 and r = 6 a typical result is (1, 2, 2, 3, 4, 4).A final ranking of the n competitors will be determined in all circumstances if a strict ordering is assigned to all possible results. In the next section it is shown that the number or results is . Of course only some strict orderings of this set of results will be feasible in that there are criteria which a final ranking should satisfy. For example, (1, 1, ..., 1) should clearly be ranked first in any feasible ranking. 
Rankings and Ranking Functions. Canadian journal of mathematics, Tome 33 (1981) no. 2, pp. 395-399. doi: 10.4153/CJM-1981-033-0
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