9 problems

Let $M$ be a connected matroid of rank $k$ on $n$ elements. Let $E_M(t)$ denote its Ehrhart polynomial, and let $M_{\rm min}$ and $U_{k,n}$ denote respectively the minimal matroid…

Bombieri's odd-even refinement. If

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…

Coefficient inequality conjecture. For every integer $i$ with $1\le i\le\left\lfloor\frac{d}{2}\right\rfloor$, one has

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…