16 problems

Non-modest poset conjecture. There is a fixed poset $P$ such that

Let $Q_n$ denote the diagonal poset on $n$ elements, and let $R(Q_n,Q_n)$ be its two-colour Ramsey number. For a positive integer $L$, consider the colouring construction in which…

Fixed-dimensional Boolean-lattice conjecture. For every fixed $m\in\mathbb{N}$,

Fixed-poset asymptotic conjecture. For $n\in\mathbb{N}$ and fixed $P$,

Weak-versus-induced conjecture. For every $n\in\mathbb{N}$,

Axenovich–author conjecture. For any $\varepsilon>0$, there is a large enough $m_0$ such that for any $m,n\in\mathbb{N}$ with $n\ge m\ge m_0$,

Lu–Thompson conjecture.

Diagonal growth conjecture.

Sublinear improvement conjecture. For any fixed poset $P$ and large $n$,

Let $Q_n$ denote the Boolean lattice of subsets of an $n$-element set, let $R(Q_n,Q_n)$ be the induced poset Ramsey number, and let $R^{\mathrm{w}}(Q_n,Q_n)$ be the weak poset Rams…

Let $Q_n$ denote the Boolean lattice of subsets of an $n$-element set, and let $R(Q_m,Q_n)$ be the induced poset Ramsey number. Fixed-$m$ asymptotic conjecture. For fixed…

Let $Q_n$ denote the Boolean lattice of subsets of an $n$-element set, let $R(Q_m,Q_n)$ be the induced poset Ramsey number, and let $\varepsilon>0$. Subpolynomial-factor conjecture…

Let $Q_n$ denote the Boolean lattice of subsets of an $n$-element set, and let $R(Q_m,Q_n)$ be the induced poset Ramsey number for the pair $(Q_m,Q_n)$. Lu–Thompson's conjecture. F…

Boolean-lattice asymptotic conjecture. For every fixed $m\in\mathbb{N}$,

Fixed-poset asymptotic conjecture. For every fixed poset $P$,

Let $Q_m$ and $Q_n$ denote Boolean lattices of dimensions $m$ and $n$, respectively, and let $R(Q_m,Q_n)$ be the least integer $N$ such that every red-blue coloring of the Boolean…