Counting self-conjugate (s, s+ 1 , s+ 2) -core partitions

Hyunsoo Cho, Ji Sun Huh, Jaebum Sohn

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


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 languageEnglish
Pages (from-to)163-174
Number of pages12
JournalRamanujan Journal
Issue number1
Publication statusPublished - 2021 May

Bibliographical note

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All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory


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