Monotonicity conjecture for successive polyomino counts

Let P(n)P(n) denote the number of polyominoes with nn cells. Successive-ratio monotonicity conjecture. The sequence

P(n)P(n1)\frac{P(n)}{P(n-1)}

is increasing. The conjecture is motivated by the available values of P(n)P(n) and is stronger than the known fact that the limit of P(n)/P(n1)P(n)/P(n-1) exists and equals Klarner's constant. No proof or disproof is supplied in the source.

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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