# Counterexamples to conjectures about Subset Takeaway and counting linear extensions of a Boolean lattice

## TL;DR

This paper introduces an efficient recursive algorithm for posets, demonstrating its utility by disproving conjectures about the Subset Takeaway game and calculating linear extensions of Boolean lattices.

## Contribution

The paper presents a novel recursive algorithm for poset functions, enabling the disproof of existing conjectures and precise enumeration of linear extensions in complex lattices.

## Key findings

- Disproved conjectures about Subset Takeaway game.
- Successfully computed linear extensions of a 7-cube lattice.
- Demonstrated algorithm's efficiency in poset analysis.

## Abstract

We develop an algorithm for efficiently computing recursively defined functions on posets. We illustrate this algorithm by disproving conjectures about the game Subset Takeaway (Chomp on a hypercube) and computing the number of linear extensions of the lattice of a 7-cube and related lattices.