5 problems

Interval-complement conjecture. Every such complement is an interval of $L$.

Let $g_3^{\ast}(n)$, $g_3^{\ast\ast}(n)$, and $g_r(n)$ be the functions defined earlier in the paper, and let $\mathbb{N}^{\geq k}=\{n\in\mathbb{N}:n\geq k\}$. Equality and strict…

Let $L$ be a finite lattice with $n$ elements, and write ${\rm Con}(L)$ for its congruence lattice. Let ${\cal L}_k$, ${\cal L}_3\boxplus {\cal L}_5$, and…

The fifth-largest-value conjecture. The set of lattices attaining the fifth-largest congruence count is

Let $L$ be a finite modular lattice, let $K[L]$ be the polynomial ring over a field $K$ whose variables are the elements of $L$, and let $I_L$ be the ideal generated by the binomia…