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.
UR - http://www.scopus.com/inward/record.url?scp=85088639185&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85088639185&partnerID=8YFLogxK
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 -