Sizes of simultaneous core partitions
نویسندگان
چکیده
There is a well-studied correspondence by Jaclyn Anderson between partitions that avoid hooks of length s or t and certain binary strings s+t. Using this map, we prove the total size random partition kind converges in law to Watson's U^2 distribution, as conjectured Doron Zeilberger.
منابع مشابه
Results and conjectures on simultaneous core partitions
An n-core partition is an integer partition whose Young diagram contains no hook lengths equal to n. We consider partitions that are simultaneously a-core and b-core for two relatively prime integers a and b, which correspond to abacus diagrams and the combinatorics of the affine symmetric group (type A). We observe that self-conjugate simultaneous core partitions correspond to type C combinato...
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Let λ = (λ1, λ2, . . . , λm) be a partition of size n, i.e., the λi are weakly decreasing positive integers summing to n. We can represent λ by means of its Young (or Ferrers) diagram, which consists of a collection of left-justified rows where row i contains λi cells. To each of these cells B one associates its hook length, that is, the number of cells in the Young diagram of λ that are direct...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2022
ISSN: ['0097-3165', '1096-0899']
DOI: https://doi.org/10.1016/j.jcta.2021.105536