Conjectural modulo-11 congruences for overcolored partition k-tuples
Prove the conjectured modulo-11 congruences \(\bar{b}^8_{5,1}(22n+11)\), \(\bar{b}^4_{4,3}(22n+11)\), \(\bar{b}^5_{1,4}(22n+11)\), \(\bar{b}^{10}_{1,4}(22n+11)\), and \(\bar{b}^4_{4,1}(22n+11)\) vanish modulo 11 for all \(n\ge0\).
References
\begin{conjecture} For all $n\ge 0$, \bar{b}8_{5,1}(22n+11)\equiv 0\pmod{11},\quad \bar{b}4_{4,3}(22n+11)\equiv 0\pmod{11},\quad \bar{b}5_{1,4}(22n+11)\equiv 0\pmod{11},\quad \bar{b}{10}_{1,4}(22n+11)\equiv 0\pmod{11},\quad \bar{b}4_{4,1}(22n+11)\equiv 0\pmod{11}. \end{conjecture}
— Overcolored Partition $k$-tuples Restricted by Parity of the Parts
(2609.03926 - Thejitha et al., 3 Sep 2026) in Section 6s7, Concluding remarks, item 3, third conjecture