We consider bipartitions subject to certain restrictions and show that be(m, n)≥bo(m, n), where be(m, n) (respectively, bo(m, n)) denotes the number of these partitions with an even (respectively, odd) number of even parts. Our principal tool is a lemma concerning the non-negativity of the coefficients of a certain rational function. As another corollary of this lemma, we deduce an inequality between the rank-counting numbers, N(r, m, n).
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics