The (s,s + d,…,s + pd)-core partitions and the rational Motzkin paths

Hyunsoo Cho, Ji Sun Huh, Jaebum Sohn

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Abstract

In this paper, we propose an (s+d,d)-abacus for (s,s+d,…,s+pd)-core partitions and establish a bijection between the (s,s+d,…,s+pd)-core partitions and the rational Motzkin paths of type (s+d,−d). This result not only gives a lattice path interpretation of the (s,s+d,…,s+pd)-core partitions but also counts them with an explicit formula. Also we enumerate (s,s+1,…,s+p)-core partitions with k corners and self-conjugate (s,s+1,…,s+p)-core partitions.

Original languageEnglish
Article number102096
JournalAdvances in Applied Mathematics
Volume121
DOIs
Publication statusPublished - 2020 Oct

Bibliographical note

Funding Information:
The authors would like to thank Byungchan Kim and the referee for their careful reading and valuable comments on this paper. Hyunsoo Cho was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (Grant No. 2019R1A6A1A11051177). JiSun Huh was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1C1C1A01008524). Jaebum Sohn was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1F1A1A01066216).

Funding Information:
The authors would like to thank Byungchan Kim and the referee for their careful reading and valuable comments on this paper. Hyunsoo Cho was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (Grant No. 2019R1A6A1A11051177 ). JiSun Huh was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1C1C1A01008524 ). Jaebum Sohn was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1F1A1A01066216 ).

Publisher Copyright:
© 2020 Elsevier Inc.

All Science Journal Classification (ASJC) codes

  • Applied Mathematics

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