TY - JOUR

T1 - Counting self-conjugate (s, s+ 1 , s+ 2) -core partitions

AU - Cho, Hyunsoo

AU - Huh, Ji Sun

AU - Sohn, Jaebum

N1 - Publisher Copyright:
© 2020, Springer Science+Business Media, LLC, part of Springer Nature.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

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U2 - 10.1007/s11139-020-00300-y

DO - 10.1007/s11139-020-00300-y

M3 - Article

AN - SCOPUS:85088639185

JO - Ramanujan Journal

JF - Ramanujan Journal

SN - 1382-4090

ER -