2013/03/10 by Alexander Berkovich, Berkovich, Alexander, Keith Grizzell +1
Mathematics · #05A17 #05A20 #11P83 #11P84 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #Primary 11P82 #Secondary 11P81 #math.CO #math.NT #msc:05A17 #msc:05A20 #msc:11P81 #msc:11P82 #msc:11P83 #msc:11P84
paper · pdf · doi:10.48550/arxiv.1303.2362
10 pages
arxiv created 2013/03/10 · arxiv updated 2013/03/12
In this paper we provide proofs of two new theorems that provide a broad class of partition inequalities and that illustrate a naïve version of Andrews' anti-telescoping technique quite well. These new theorems also put to rest any notion that including parts of size 1 is somehow necessary in order to have a valid irreducible partition inequality. In addition, we prove (as a lemma to one of the theorems) a rather nontrivial class of rational functions of three variables has entirely nonnegative power series coefficients.