论文标题
Turán的不平等现象$ k $ -Diamond分区功能
Turán inequalities for the broken $k$-diamond partition function
论文作者
论文摘要
我们为Andrews和Paule的破碎$ K $ -Diamond分区功能$δ_K（n）$获得了渐近公式，其中$ k = 1 $或$ 2 $。基于这个渐近公式，我们得出$δ_k（n）$满足$ d $ d $turán的订单，当$ d \ geq 1 $ $ d \ geq 1 $，并且在使用Griffin，Ono，Rolen和Zagier的一般结果时，$ d \ geq 1 $，对于足够大的$ n $。我们还表明，Andrews and Paule的损坏$ K $ -Diamond分区函数$δ_K（n）$是log-concave，当$ n \ geq 1 $时，$ k = 1 $和$ 2 $。这导致$Δ_K（a）δ_k（b）\geΔ_k（a+b）$ for $ a，b \ ge 1 $当$ k = 1 $和$ 2 $。
We obtain an asymptotic formula for Andrews and Paule's broken $k$-diamond partition function $Δ_k(n)$ where $k=1$ or $2$. Based on this asymptotic formula, we derive that $Δ_k(n)$ satisfies the order $d$ Turán inequalities for $d\geq 1$ and for sufficiently large $n$ when $k=1$ and $ 2$ by using a general result of Griffin, Ono, Rolen and Zagier. We also show that Andrews and Paule's broken $k$-diamond partition function $Δ_k(n)$ is log-concave for $n\geq 1$ when $k=1$ and $2$. This leads to $Δ_k(a)Δ_k(b)\geΔ_k(a+b)$ for $a,b\ge 1$ when $k=1$ and $ 2$.
