Laguerre inequality and determinantal inequality for the broken k-diamond partition function

2023/05/29 by Yang, Eve Y. Y.
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2305.17864

Abstract

In 2007, Andrews and Paule introduced the broken k-diamond partition function Δ_k(n), which has received a lot of researches on the arithmetic propertises. In this paper, we will prove the broken k-diamond partition function satisfies the Laguerre inequalities of order 2 and the determinantal inequalities of order 3 for k=1 or 2. Moreover, we conjectured the thresholds for the Laguerre inequalities of order m and the positivity of m-order determinants for 4≤ m≤ 14 for the broken k-diamond partition function when k=1 or 2.

Related

• Inequalities for the Broken k-Diamond Partition Function
• Turán inequalities for the broken k-diamond partition function
• Laguerre inequalities and determinantal inequalities for the finite difference of the partition functions
• New congruences for broken k-diamond partitions
• Congruences for Broken k-Diamond Partitions