TY - JOUR
AU - Campbell, John
AU - Chern, Shane
PY - 2023/06/25
Y2 - 2024/06/16
TI - Nearly self-conjugate integer partitions
JF - New Zealand Journal of Mathematics
JA - NZ J Math
VL - 54
IS -
SE - Articles
DO - 10.53733/217
UR - https://nzjmath.org/index.php/NZJMATH/article/view/217
SP - 1--7
AB - <p>We investigate integer partitions $\lambda$ of $n$ that are nearly self-conjugate in the sense that there are $n - 1$ overlapping cells among the Ferrers diagram of $\lambda$ and its transpose, by establishing a correspondence, through the method of combinatorial telescoping, to partitions of $n$ in which (i).~there exists at least one even part; (ii).~any even part is of size $2$; (iii).~the odd parts are distinct; and (iv).~no odd part is of size $1$. In particular, this correspondence confirms a conjecture that had been given in the OEIS.</p>
ER -