논문
On the number of even and odd strings along the overpartitions of $n$
- 저자Byungchan Kim, Eunmi Kim, Jeehyeon Seo
- 학술지Archiv der Mathematik 102(4), 357-368
- 등재유형
- 게재일자(2014)
Recently, Andrews, Chan, Kim and Osburn introduced the even strings and the odd strings in the overpartitions. We show that their conjecture
\[
A_k (n) \ge B_k (n)
\]
holds for large enough positive integers $n$, where $A_k (n)$ (resp. $B_k (n)$) is the number of odd (resp. even) strings along the overpartitions of $n$. We introduce $m$-strings and show how this new combinatorial object is related with another positivity conjecture of Andrews, Chan, Kim, and Osburn. Finally, we confirm that the positivity conjecture is also true for large enough integers.
Recently, Andrews, Chan, Kim and Osburn introduced the even strings and the odd strings in the overpartitions. We show that their conjecture
\[
A_k (n) \ge B_k (n)
\]
holds for large enough positive integers $n$, where $A_k (n)$ (resp. $B_k (n)$) is the number of odd (resp. even) strings along the overpartitions of $n$. We introduce $m$-strings and show how this new combinatorial object is related with another positivity conjecture of Andrews, Chan, Kim, and Osburn. Finally, we confirm that the positivity conjecture is also true for large enough integers.
