11 problems

For any nonnegative integer $n$, define … Let $Q_2(n)$ denote the partition function in the source. Weaker $Q_2$ truncated-sum inequality. For $n\geqslant0$ and $k>0$, … The source…

For any integer $n$, define … Let $b_6(n)$ denote the $6$-regular partition function, and let $(\rho_j)_{j\geqslant0}$ be the coefficient sequence in the source. 6-regular partitio…

For any integer $n$, define … Let $b_6(n)$ denote the $6$-regular partition function. 6-regular partition inequality. For $n\geqslant0$ and $k>0$, … with strict inequality if…

For $n,k\geqslant0$, let $p(n)$ denote Euler's partition function, let $Q_2(n)$ denote the partition function used in the source, and let $(\rho_j)_{j\geqslant0}$ be the coefficien…

Contractive dual coefficient conjecture. The inequality

Burbea's conjecture. The inequality

Let $n$ be a positive integer, and write the resulting formal power series in $q$ as a polynomial or power series with coefficients in the relevant coefficient ring. Prellberg–Stan…

Bombieri's odd-even refinement. If

Let $S$ be the class of normalized univalent functions in the unit disk, with … and, for $r\in[0,1]$, let $(C_r)$ denote the statement … for every $f\in S$ and every $n\ge 2$. Seco…

Let $S$ be the class of normalized univalent functions in the unit disk, with … and, for $t\in[0,1]$, let $(B_t)$ denote the statement … for every $f\in S$ and every $n\ge 2$. Firs…

Let $F_{\lambda}(q)=\sum_{i=0}^{d}c_iq^i$ be the rank-generating function for partitions contained inside a partition $\lambda$. The polynomial is flawless if $c_i\le c_{d-i}$ for…