Integer partitions and exclusion statistics: Limit shapes and the largest part of Young diagrams
نویسندگان
چکیده
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 = P i nii 1/ν with ν > 0 where ni is the number of times the part i appears. Journal-ref: J. Stat. Mech. (2007) P10001
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