5 problems

Fix an integer $k\geq1$, and let $p_{k,1}(2,n)$ be the restricted rectangle-partition function from the paper. For each $j$, write $[r_{i,j,0},r_{i,j,1},\ldots,r_{i,j,j-1}]_j$ for…

Fix an integer $k\geq 1$. Let $p_{k,1}(2,n)$ denote the number of partitions of the rectangle $2\times n$ using the block-size restrictions indexed by $k$ and $1$ in the paper. A f…

Let $p(3,n)$ denote the number of partitions of a $3\times n$ rectangle into permitted rectangular blocks, as defined in the paper. Asymptotic form conjecture. There exist constant…

Let $S$ be a square, and let $k$ be the number of rectangles in a partition. A proper perfect Mondrian partition is the paper's specified partition of $S$ into $k$ pairwise non-con…

A proper perfect Mondrian partition of a square is a partition into pairwise non-congruent rectangles of equal area, satisfying the additional propriety condition defined by the pa…