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Published online by Cambridge University Press: 15 September 2014
(1) Having formed from n things all possible sets of r, we may subject each of the Cn,r sets to the test of fulfilling one or more conditions, and so obtain a reduced number possessing a special characterisation. The present note deals with a few instances of this in which the reduced number is of the same algebraical form as the full number, that is to say, is a combinatorial Ca,b.
page 102 note * An analogous peculiarity appears in the well-known theorem that the number of combinations of n things taken r at a time when repetitions are allowed is the same as the number of combinations of n − r + 1 things with repetitions debarred, i.e., is equal to Cn−r+1,r.
