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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2024.4
- 수록면
- 345 - 352 (8page)
- DOI
- 10.4134/CKMS.c230214
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초록· 키워드
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We introduce a new class of bi-partition function $c_k(n)$, which counts the number of bi-color partitions of $n$ in which the second color only appears at the parts that are multiples of $k$. We consider two partitions to be the same if they can be obtained by switching the color of parts that are congruent to zero modulo $k$. We show that the generating function for $c_k(n)$ involves the partial theta function and obtain the following congruences: \begin{align*} c_2 (27n+26) &\equiv 0 \pmod{3} \\ \intertext{and} c_3 (4n + 2 ) &\equiv 0 \pmod{2}. \end{align*}
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