| Let fk(n, m) denote the number of ways of selecting m objects from n objects arrayed in a line with no two selected having k-spparations (i.e., having exactly k-objects between them) .If the objects are arranged in a circle, the corresponding number is denoted by gk(n, m) . Kaplansky first published a derivation by recurrence relation for k - 0. Recently, Konvalina derived the enumerative formulae for k =1 by using the similar method . For a general k, this problem is somehow more difficult and complicated. |
