Results on bar-core partitions, core shifted Young diagrams, and doubled distinct cores
| Autor: | Cho, Hyunsoo, Huh, JiSun, Nam, Hayan, Sohn, Jaebum |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Simultaneous bar-cores, core shifted Young diagrams (or CSYDs), and doubled distinct cores have been studied since Morris and Yaseen introduced the concept of bar-cores. In this paper, our goal is to give a formula for the number of these core partitions on $(s,t)$-cores and $(s,s+d,s+2d)$-cores for the remaining cases that are not covered yet. In order to achieve this goal, we observe a characterization of $\bar{s}$-core partitions to obtain characterizations of doubled distinct $s$-core partitions and $s$-CSYDs. By using them, we construct $NE$ lattice path interpretations of these core partitions on $(s,t)$-cores. Also, we give free Motzkin path interpretations of these core partitions on $(s,s+d,s+2d)$-cores. Comment: 19 pages, 4 figures |
| Databáze: | arXiv |
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