We give a complete characterization of the parity of $b_8(n)$, the number of $8$-regular partitions of $n$. Namely, we prove that $b_8(n)$ is odd precisely when $24n+7$ has the form $p^{4a+1}m^2$ with $p$ prime and $p\nmid m$.
Cherubini, G., Mercuri, P. (2024). Parity of the 8-regular partition function. RAMANUJAN JOURNAL, 63(3), 715-722 [10.1007/s11139-023-00784-4].
Parity of the 8-regular partition function
Mercuri P.
2024-03-01
Abstract
We give a complete characterization of the parity of $b_8(n)$, the number of $8$-regular partitions of $n$. Namely, we prove that $b_8(n)$ is odd precisely when $24n+7$ has the form $p^{4a+1}m^2$ with $p$ prime and $p\nmid m$.
File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
s11139-023-00784-4.pdf
Solo gestori archvio
Tipologia:
Versione Editoriale
Dimensione
198.38 kB
Formato
Adobe PDF
|
198.38 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
