Monotonicity conjecture for the inconstructible-polyomino ratio
Monotonicity conjecture for the inconstructible-polyomino ratio
Let be the number of polyominoes with cells. A polyomino is constructible if it is the concatenation of two polyominoes of smaller sizes, and inconstructible otherwise; let denote the number of inconstructible polyominoes with cells. Inconstructible-polyomino ratio conjecture. The sequence
is decreasing. This conjecture is based on the available values of the sequences, computed up to 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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