Monotonicity conjecture for the inconstructible-polyomino ratio

From papers

Let P(n)P(n) be the number of polyominoes with nn cells. A polyomino is constructible if it is the concatenation of two polyominoes of smaller sizes, and inconstructible otherwise; let Q(n)Q(n) denote the number of inconstructible polyominoes with nn cells. Inconstructible-polyomino ratio conjecture. The sequence

Q(n)P(n)\frac{Q(n)}{P(n)}

is decreasing. This conjecture is based on the available values of the sequences, computed up to n=56n=56 in the source. Its resolution would provide the conjectural monotonicity needed for the paper's conditional upper-bound discussion, but no proof or disproof is given.

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Sources & referencesView supporting material

Primary source

Vuong Bui, “An asymptotic lower bound on the number of polyominoes”, arXiv:2211.14909 (2023).

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