### Abstract

We are concerned with counting self-conjugate (s, s+ 1 , s+ 2) -core partitions. A Motzkin path of length n is a path from (0, 0) to (n, 0) which stays weakly above the x-axis and consists of the up U= (1 , 1) , down D= (1 , - 1) , and flat F= (1 , 0) steps. We say that a Motzkin path of length n is symmetric if its reflection about the line x= n/ 2 is itself. In this paper, we show that the number of self-conjugate (s, s+ 1 , s+ 2) -cores is equal to the number of symmetric Motzkin paths of length s, and give a closed formula for this number.

Original language | English |
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Journal | Ramanujan Journal |

DOIs | |

Publication status | Accepted/In press - 2020 |

### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

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## Cite this

Cho, H., Huh, J. S., & Sohn, J. (Accepted/In press). Counting self-conjugate (s, s+ 1 , s+ 2) -core partitions.

*Ramanujan Journal*. https://doi.org/10.1007/s11139-020-00300-y