Closed form expressions for the iterated floor function

@article{Redish1990ClosedFE,
  title={Closed form expressions for the iterated floor function},
  author={K. A. Redish and William F. Smyth},
  journal={Discrete Mathematics},
  year={1990},
  volume={91},
  pages={317-321}
}
Redish, K.A. and W.F. Smyth, Closed from expressions for the iterated floor function, Discrete Mathematics 91 (1991) 317-321. For positive integers k, r, and n 2 k + 1, the iterated floor function f_ is defined by f,,,(k + 1) = r; f*.,(n) = [&fk,,(n 111, n > k + 1. A special case (k = r = 3) of this function occurs as an upper bound on the number of 3-subsets, excluding tetrahedra, of an n-set (Turan’s problem). For certain values of k and r, this note establishes closed form expressions for fk… CONTINUE READING