6 problems

Postnikov–Stanley polynomials are a class of polynomials associated with permutations. A polynomial is M-convex when the set of exponent vectors of its monomials satisfies the disc…

For $d\geq 6$, define … Here $\mathbb{R}_{\geq0}[a_1^2+a_2^2,a_1^2a_2^2]$ denotes the polynomials in the two displayed generators with nonnegative real coefficients. Nonnegative in…

Matching-coefficient negativity conjecture. The coefficient of $\mu$ in $Y$ is negative. This coefficient-level assertion is used to establish the predicted sign in type $D_n$; it…

Alweiss's non-partition-regularity conjecture. There exists $n$ such that, for every $d\in\mathbb{N}$, the pattern

For positive integers $k$ and a positive real number $0<\delta<1$, define … For $a\in K[n]$, let $\gamma\subset[N]$ and interpret $\gamma^r$ as the corresponding $r$-fold Cartesian…

Almkvist's conjecture. The polynomial $f_{n,r}(q)$ is an ${\rm A}$-polynomial if either $r$ is even and $n\ge 1$, or $r$ is odd and $n\ge 11$. This conjecture gives sufficient cond…