4 problems

Let $s_n(z)$ be the polynomial defined from the Bazhanov–Mangazeev polynomial by … Let $p_n$ be the polynomial introduced by Mangazeev and Bazhanov, indexed by $n\in\mathbb Z$. Man…

Bazhanov–Mangazeev conjecture. Specializations of these polynomials are tau functions of Painlevé VI, constructed from one of Picard's algebraic solutions by a sequence of Bäcklund…

Let $Q_n$ denote the $n$th Yablonskii–Vorob'ev polynomial, defined by $Q_0=1$, $Q_1=z$, and … For a real number $x$, let $[x]$ denote its integer part. Clarkson's conjecture. The n…

At $\eta=\pi/3$, set $x=-1/2$ and $y=\zeta/2$, and let $p_k(z)$ denote the polynomials related to those of Bazhanov and Mangazeev for the spin-$1/2$ XYZ chain. For odd $N=2n+1$, le…