Geodesic
The asymptotic normality of \((s,s+1)\)-cores with distinct parts
János Komlós1 ; Emily Sergel2 ; Gábor Tusnády3
1Rutgers University
2University of Pennsylvania
3MTA Rényi Alfréd Matematikai Kutató Intézet
The electronic journal of combinatorics, Tome 27 (2020) no. 1
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Simultaneous core partitions are important objects in algebraic combinatorics. Recently there has been interest in studying the distribution of sizes among all $(s,t)$-cores for coprime $s$ and $t$. Zaleski (2017) gave strong evidence that when we restrict our attention to $(s,s+1)$-cores with distinct parts, the resulting distribution is approximately normal. We prove his conjecture by applying the Combinatorial Central Limit Theorem and mixing the resulting normal distributions.
DOI : 10.37236/8770
Classification : 05A16, 05A17
Mots-clés : simultaneous core partitions

János Komlós  1   ; Emily Sergel  2   ; Gábor Tusnády  3

1 Rutgers University
2 University of Pennsylvania
3 MTA Rényi Alfréd Matematikai Kutató Intézet 
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     title = {The asymptotic normality of \((s,s+1)\)-cores with distinct parts},
     journal = {The electronic journal of combinatorics},
     year = {2020},
     volume = {27},
     number = {1},
     doi = {10.37236/8770},
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     url = {http://geodesic.mathdoc.fr/articles/10.37236/8770/}
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János Komlós; Emily Sergel; Gábor Tusnády. The asymptotic normality of \((s,s+1)\)-cores with distinct parts. The electronic journal of combinatorics, Tome 27 (2020) no. 1. doi: 10.37236/8770

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