Integer partitions and exclusion statistics: Limit shapes and the largest part of Young diagrams

Details Integer partitions and exclusion statistics: Limit shapes and the largest part of Young diagrams Integer partitions and exclusion statistics: Limit shapes and the largest part of Young diagrams

2007-07-16

arxiv.org/abs/0707.2312v2

J. Stat. Mech. (2007) P10001

Physics

Condensed Matter

Statistical Mechanics

12 pages, 4 figures (minor corrections, a note and some references added)

Scientific paper

10.1088/1742-5468/2007/10/P10001

We compute the limit shapes of the Young diagrams of the minimal difference $p$ partitions and provide a simple physical interpretation for the limit shapes. We also calculate the asymptotic distribution of the largest part of the Young diagram and show that the scaled distribution has a Gumbel form for all $p$. This Gumbel statistics for the largest part remains unchanged even for general partitions of the form $E=\sum_i n_i i^{1/\nu}$ with $\nu>0$ where $n_i$ is the number of times the part $i$ appears.

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