Average size of a self-conjugate $(s,t)$-core partition
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- by William Y. C. Chen, Harry H. Y. Huang and Larry X. W. Wang PDF
- Proc. Amer. Math. Soc. 144 (2016), 1391-1399 Request permission
Abstract:
Armstrong, Hanusa and Jones conjectured that if $s,t$ are coprime integers, then the average size of an $(s,t)$-core partition and the average size of a self-conjugate $(s,t)$-core partition are both equal to $\frac {(s+t+1)(s-1)(t-1)}{24}$. Stanley and Zanello showed that the average size of an $(s,s+1)$-core partition equals $\binom {s+1}{3}/2$. Based on a bijection of Ford, Mai and Sze between self-conjugate $(s,t)$-core partitions and lattice paths in an $\lfloor \frac {s}{2} \rfloor \times \lfloor \frac {t}{2}\rfloor$ rectangle, we obtain the average size of a self-conjugate $(s,t)$-core partition as conjectured by Armstrong, Hanusa and Jones.References
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Additional Information
- William Y. C. Chen
- Affiliation: Center for Applied Mathematics, Tianjin University, Tianjin 300072, People’s Republic of China
- MR Author ID: 232802
- Email: chenyc@tju.edu.cn
- Harry H. Y. Huang
- Affiliation: Center for Combinatorics, LPMC-TJKLC, Nankai University, Tianjin 300071, People’s Republic of China
- Email: haoyangh@mail.nankai.edu.cn
- Larry X. W. Wang
- Affiliation: Center for Combinatorics, LPMC-TJKLC, Nankai University, Tianjin 300071, People’s Republic of China
- MR Author ID: 845775
- Email: wsw82@nankai.edu.cn
- Received by editor(s): May 11, 2014
- Received by editor(s) in revised form: January 1, 2015
- Published electronically: December 21, 2015
- Additional Notes: We wish to thank the referee for helpful suggestions. This work was supported by the 973 Project, the PCSIRT Project of the Ministry of Education and the National Science Foundation of China.
- Communicated by: Patricia Hersh
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 1391-1399
- MSC (2010): Primary 05A17, 05A15
- DOI: https://doi.org/10.1090/proc/12729
- MathSciNet review: 3451218