Infinite distributivity of meet over join for a principal funcoid ★★

Author(s): Porton

\begin{conjecture} $f \sqcap \bigsqcup S = \bigsqcup \langle f \sqcap \rangle^{\ast} S$ for principal funcoid $f$ and a set $S$ of funcoids of appropriate sources and destinations. \end{conjecture}

Keywords: distributivity; principal funcoid

Entourages of a composition of funcoids ★★

Author(s): Porton

\begin{conjecture} $\forall H \in \operatorname{up} (g \circ f) \exists F \in \operatorname{up} f, G \in \operatorname{up} g : H \sqsupseteq G \circ F$ for every composable funcoids $f$ and $g$. \end{conjecture}

Keywords: composition of funcoids; funcoids

Weak saturation of the cube in the clique

Author(s): Morrison; Noel

\begin{problem} % Enter your conjecture in LaTeX % You may change "conjecture" to "question" or "problem" if you prefer. Determine $\text{wsat}(K_n,Q_3)$. \end{problem}

Keywords: bootstrap percolation; hypercube; Weak saturation

Convex Equipartitions with Extreme Perimeter ★★

Author(s): Nandakumar

To divide a given 2D convex region C into a specified number n of convex pieces all of equal area (perimeters could be different) such that the total perimeter of pieces is (1) maximized (2) minimized.

Remark: It appears maximizing the total perimeter is the easier problem.

Keywords: convex equipartition