Bill Sands

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math.CO2025

Cutsets in $P (X)$

John Ginsburg, Bill Sands

For any set $X$ , $P (X)$ denotes the collection of all subsets of $X$ , ordered by inclusion. A {\it cutset} in $P (X)$ is a subset of $P (X)$ which me…

math.CO2024

Colouring of Maximal $F$ -free Subsets

Bill Sands

For each finite poset $F$ with $∣ F ∣ > 1$ , $χ_{a c} (F)$ denotes the smallest integer $n$ (if it exists) such that the elements of every finite poset $P$ with $∣ P ∣ > 1$ can be coloure…

math.CO2024

Covering Distributive Lattices by Intervals

Dwight Duffus, Bill Sands

We consider the convex subset $[A, B]$ of all elements between two levels $A$ and $B$ of a finite distributive lattice, as a union of (or covered by) intervals $[a, b]$ . A 1988 resul…

Cutsets in P(X)

Colouring of Maximal F-free Subsets

Covering Distributive Lattices by Intervals

Cutsets in $P (X)$

Colouring of Maximal $F$ -free Subsets