Geodesic
Core partitions with distinct parts
Huan Xiong1
1Université de Strasbourg
The electronic journal of combinatorics, Tome 25 (2018) no. 1

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Zbl arXiv
Simultaneous core partitions have attracted much attention since Anderson's work on the number of $(t_1,t_2)$-core partitions. In this paper we focus on simultaneous core partitions with distinct parts. The generating function of $t$-core partitions with distinct parts is obtained. We also prove results on the number, the largest size and the average size of $(t, t + 1)$-core partitions with distinct parts. This gives a complete answer to a conjecture of Amdeberhan, which is partly and independently proved by Straub, Nath and Sellers, and Zaleski recently.
DOI : 10.37236/6907
Classification : 05A17, 11P81
Mots-clés : simultaneous core partition, distinct part, hook length, largest size, average size

Huan Xiong  1

1 Université de Strasbourg 
Huan Xiong. Core partitions with distinct parts. The electronic journal of combinatorics, Tome 25 (2018) no. 1. doi: 10.37236/6907
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     author = {Huan Xiong},
     title = {Core partitions with distinct parts},
     journal = {The electronic journal of combinatorics},
     year = {2018},
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     number = {1},
     doi = {10.37236/6907},
     zbl = {1392.05011},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/6907/}
}
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