5 problems

Let an equilateral triangle and a square have the same area, and consider dissections into finitely many pieces that may be rearranged, with pieces allowed to be turned over. Three…

The multiples-of-factorial conjecture. For any $n\in\mathbb{Z}_{>3}$, if $P,Q\subset\mathbb{R}^n$ are two arbitrary Ehrhart-equivalent integral $n$-polytopes, then

The factorial dilation conjecture. For any $n\in\mathbb{Z}_{\ge 1}$, if $P,Q\subset\mathbb{R}^n$ are arbitrary Ehrhart-equivalent integral $n$-polytopes, then they are…

Ehrhart-function conjecture. There exists an equidecomposability relation $\mathcal{F}:(S,\mathcal{T})\to(S',\mathcal{T}')$ if and only if

Let Ehrhart-equivalent rational polytopes be rational polytopes whose Ehrhart functions agree. Discrete equidecomposability is allowed to use an arbitrary number of simplices, and…