34 problems

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

Let $B_n$ be the Boolean lattice of all subsets of an $n$-element set, ordered by containment, and let $G$ be a subgroup of its automorphism group. The quotient $B_n/G$ consists of…

Let $\mu$ be a CNA+ measure on the Boolean lattice $\mathcal{B}_n$, with coordinate indicators $X_1,\ldots,X_n$. Conditional-cover conjecture. The conditional distribution on…

Let $B_n$ denote the Boolean lattice of subsets of an $n$-element set, and let a poset be nice when its incomparability graph has the nice property. Boolean-lattice niceness conjec…

Let $[n]=\{1,\ldots,n\}$, let $2^{[n]}$ be its power set, and let $G_{\mathcal{F}}$ be the graph whose vertex set is a family $\mathcal{F}\subseteq 2^{[n]}$, with two vertices adja…

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 $n$,

Griggs's conjecture. The incomparability graph $\operatorname{inc}(B_n)$ of the Boolean lattice $B_n$ is nice.

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…

Non-Cancelling Intersections Conjecture. Whenever the measure of a union of sets can be expressed using the measures of some of their intersections through the inclusion-exclusion…

Let $P$ be a poset, and let $\mathop{}\\!\operatorname{extsat}(n,P)$ denote the minimum size of an external $P$-saturated family for the Boolean lattice ${\mathcal B}_n$, as define…

For a finite poset $P$, let an external $P$-saturated family for the Boolean lattice ${\mathcal B}_n$ be a family as defined in the paper, and let…

Let $\mathsf B_{1000}$ be the Boolean lattice on $1000$ generators, and call a 50-dimensional vector $(h_1,\dots,h_{50})$ a generating vector if its components generate…

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

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

Let $\boldsymbol{P}_i=\mathbf{V}_{m_i,m_i}$ for $1\leq i\leq k$, where $\mathbf{V}_{m_i,m_i}$ denotes the balanced V-shaped poset with $m_i$ elements on each branch. Write…

Weak Boolean lattice local dimension conjecture.