TY - CHAP

T1 - Singular Overpartitions and Partitions with Prescribed Hook Differences

AU - Seo, Seunghyun

AU - Yee, Ae Ja

N1 - Publisher Copyright:
© 2021, Springer Nature Switzerland AG.

PY - 2021

Y1 - 2021

N2 - Singular overpartitions, which are Frobenius symbols with at most one overlined entry in each row, were first introduced by Andrews in 2015. In his paper, Andrews investigated an interesting subclass of singular overpartitions, namely, (K, i)-singular overpartitions for integers K, i with 1 ≤ i < K/2. The definition of such singular overpartitions requires successive ranks, parity blocks and anchors. The concept of successive ranks was extensively generalized to hook differences by Andrews, Baxter, Bressoud, Burge, Forrester and Viennot in 1987. In this paper, employing hook differences, we generalize parity blocks. Using this combinatorial concept, we define (K, i, α, β)-singular overpartitions for positive integers α, β with α+β<K, and then we show some connections between such singular overpartitions and ordinary partitions.

AB - Singular overpartitions, which are Frobenius symbols with at most one overlined entry in each row, were first introduced by Andrews in 2015. In his paper, Andrews investigated an interesting subclass of singular overpartitions, namely, (K, i)-singular overpartitions for integers K, i with 1 ≤ i < K/2. The definition of such singular overpartitions requires successive ranks, parity blocks and anchors. The concept of successive ranks was extensively generalized to hook differences by Andrews, Baxter, Bressoud, Burge, Forrester and Viennot in 1987. In this paper, employing hook differences, we generalize parity blocks. Using this combinatorial concept, we define (K, i, α, β)-singular overpartitions for positive integers α, β with α+β<K, and then we show some connections between such singular overpartitions and ordinary partitions.

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U2 - 10.1007/978-3-030-57050-7_37

DO - 10.1007/978-3-030-57050-7_37

M3 - Chapter

AN - SCOPUS:85102001201

T3 - Trends in Mathematics

SP - 685

EP - 718

BT - Trends in Mathematics

PB - Springer Science and Business Media Deutschland GmbH

ER -