8 problems

CroSas' characterization conjecture. The independence-preserving property with $(U,V)$ defined by the transformation in characterizes generalized inverse Gaussian (GIG) laws.

Elliptic Yang–Baxter map conjecture. The map given by equations,, and is an elliptic Yang–Baxter map, with $(x,X)$ and $(y,Y)$ on the elliptic curve and subject to…

Let $\Gamma(n)$ denote the Grassmann algebra with $n$ generators, and let $\mathcal{R}_{a,b}$, $S_{a,b}$, and $T_{a,b}$ be the maps introduced in the paper, with $x_{11}$ and…

Let $H^{+,\alpha,\beta}_{I}$, $H^{+,\alpha,\beta}_{II}$, and $H^{\alpha,\beta}_{III,A}$ be the maps appearing in the theorem, with $\alpha,\beta>0$, and let the associated distribu…

Existence conjecture. For every $m$, there is a super-integrable model of class $\mathcal{O}(L^m)$, with sufficiently large local state-space size $N$.

Let $\Gamma(n)$ be a Grassmann algebra, and consider the commutative map obtained from the parametric Grassmann Yang–Baxter map by the same restriction procedure used for…

The maps under consideration are the Grassmann-extended Yang–Baxter maps in equations -- and the corresponding maps in equations --, with their invariants. Poisson involutivity con…

The paper considers matrix refactorisation and the associated Yang–Baxter maps, with formula … can be found in the case of $n\times n$ matrices, where $n>2$. The conjecture propose…