Geodesic
On a Lemma of M. Abramson
Canadian mathematical bulletin, Tome 9 (1966) no. 3, pp. 347-348

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Kaplansky's Lemma [3] states: the number of k-combinations of 1, 2,..., n with no two consecutive integers in any selection is Using this, Abramson [l; lemma 3] solves the problem: find the, number of k-combinations so that no two integers i and i+2 appear in any selection. (This is generalized by Abramson in [2].) An interesting solution, also using Kaplansky's lemma, is obtained as follows.If n = 2m, we choose s from among the m even integer s, no two consecutive, and k- s from among the m odd integers, no two consecutive. 
Jr., C.A. Church. On a Lemma of M. Abramson. Canadian mathematical bulletin, Tome 9 (1966) no. 3, pp. 347-348. doi: 10.4153/CMB-1966-043-7
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