SEQUENCES WITH INEQUALITIES

Journal of Mathematical Sciences

Abstract

Abstract We consider infinite sequences of positive numbers. The connection between log-concavity and the Bessenrodt–Ono inequality has been the focus of several papers. It has applications in the white noise distribution theory and combinatorics. We improve a recent result by Benfield and Roy and show that for the sequence of partition numbers $$\{p(n)\}$$ { p ( n ) } , Nicolas’ log-concavity result implies the result by Bessenrodt and Ono towards $$p(n) \, p(m) > p(n+m)$$ p ( n ) p ( m ) > p ( n + m ) . We provide several examples. Benfield and Roy gave a conjecture related to $$\ell $$ ℓ -ary partition numbers. We prove a part of this conjecture.

Authors 2

1. Bernhard E. Heim Aachen Lehrstuhl A für Mathematik

   RWTH Aachen University · University of Cologne

   Affiliation as printed

   Department of Mathematics and Computer Science, Division of Mathematics, University of Cologne, Weyertal 86–90, 50931, Cologne, Germany

   Lehrstuhl A für Mathematik, RWTH Aachen University, 52056, Aachen, Germany

2. Markus Neuhauser corresponding Aachen Lehrstuhl für Geometrie und Analysis

   RWTH Aachen University · Kutaisi International University

   Affiliation as printed

   Kutaisi International University, 5/7, Youth Avenue, Kutaisi, 4600, Georgia

   Lehrstuhl für Geometrie und Analysis, RWTH Aachen University, 52056, Aachen, Germany