5 problems

Let $G$ be an swm-graph. A Boolean-gated set of $G$ is a nonempty vertex subset $X$ such that every common neighbor of any two distinct vertices of $X$ belongs to $X$, and such tha…

For each positive integer $n$, let $NC_n$ be the noncrossing partition lattice, and let its orthoscheme complex be the piecewise Euclidean complex associated with the order complex…

Let $P$ be a bounded graded modular lattice. A modular lattice is a graded lattice in which, whenever $x$ and $y$ are complements in an interval $P_{zw}$ and $x$ has rank $i$ and c…

Let $P$ be a bounded graded poset, let $K$ be its diagonal link, and let $x$ and $y$ be complements in $P$. Write $v_x$ and $v_y$ for the corresponding vertices of $K$, and say tha…

Let $P$ be a bounded graded poset, and let its orthoscheme complex be the piecewise Euclidean complex obtained from the order complex of $P$ by assigning orthoscheme metrics. A spi…