Restricted bipartitions

George E. Andrews; Richard P. Lewis

doi:10.1016/S0012-365X(00)00294-6

Restricted bipartitions

George E. Andrews, Richard P. Lewis

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We consider bipartitions subject to certain restrictions and show that b_e(m, n)≥b_o(m, n), where b_e(m, n) (respectively, b_o(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).

Original language	English (US)
Pages (from-to)	85-89
Number of pages	5
Journal	Discrete Mathematics
Volume	232
Issue number	1-3
DOIs	https://doi.org/10.1016/S0012-365X(00)00294-6
State	Published - Apr 6 2001

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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abstract = "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).",

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AB - 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).

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JO - Discrete Mathematics

JF - Discrete Mathematics

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ER -

Restricted bipartitions

Abstract

All Science Journal Classification (ASJC) codes

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