4 problems

Consider any of the LEGO enumeration problems studied in the paper, and let $n$ be the number of tiles in a structure. Universal asymptotic-growth conjecture. In every such problem…

For each positive integer $n$, let $p_n(w)$ be the polynomial counting the LEGO structures made from $n$ parallel $w\times1$ tiles. Reflection-symmetry conjecture. For every…

Let $a_n$ be the number of three-dimensional LEGO structures made from $n$ $2\times4$ tiles, counted under the conventions described in the paper. Abrahamsen–Eilers conjecture. The…

Consider LEGO structures built from parallel $w\times 1$ tiles in two dimensions, and structures built from $2\times 4$ tiles in three dimensions. Let $n$ denote the number of tile…