| Integrals, Partitions, and Cellular Automata (2003) | |||||||||||||||
Abstract | |||||||||||||||
| We prove that x where f(x) is the decreasing function that satisfies f for 0 < a < b. When a is an integer and b = a + 1 we deduce several combinatorial results. These include an asymptotic formula for the number of integer partitions not having a consecutive parts, and a formula for the metastability thresholds of a class of threshold growth cellular automaton models related to bootstrap percolation. 1 | |||||||||||||||
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