Integrals, Partitions, and Cellular Automata
| dc.creator | Holroyd, Alexander E. | |
| dc.creator | Liggett, Thomas M. | |
| dc.creator | Romik, Dan | |
| dc.date | 2003-02-18 | |
| dc.date | 2003-05-06 | |
| dc.date.accessioned | 2026-07-07T04:55:23Z | |
| dc.date.available | 2026-07-07T04:55:23Z | |
| dc.description | We prove that $$\int_0^1\frac{-\log f(x)}xdx=\frac{π^2}{3ab}$$ where $f(x)$ is the decreasing function that satisfies $f^a-f^b=x^a-x^b$, 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. | |
| dc.description | Revised version. 28 pages, 2 figures | |
| dc.identifier | https://arxiv.org/abs/math/0302216 | |
| dc.identifier | http://arxiv.org/abs/math/0302216 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66561 | |
| dc.subject | Probability | |
| dc.subject | Combinatorics | |
| dc.subject | Number Theory | |
| dc.subject | 26A06; 05A17; 60C05; 60K35 | |
| dc.title | Integrals, Partitions, and Cellular Automata | |
| dc.type | text |