# Counterexamples to Conjectures About Subset Takeaway and Counting Linear Extensions of a Boolean Lattice

```@article{Brouwer2018CounterexamplesTC,
title={Counterexamples to Conjectures About Subset Takeaway and Counting Linear Extensions of a Boolean Lattice},
author={Andries E. Brouwer and J. Daniel Christensen},
journal={Order},
year={2018},
volume={35},
pages={275-281}
}```
• Published 9 February 2017
• Mathematics, Computer Science
• Order
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.
3 Citations
Chomp on generalized Kneser graphs and others
• Mathematics
Int. J. Game Theory
• 2021
Questions about which player has a winning strategy for a given graph are answered and the Nim-value is determined for the class of generalized Kneser graphs and for several families of Johnson graphs.
A vertex and edge deletion game on graphs
A conjecture of Khandhawit and Ye on the nim-values of graphs with one odd cycle is proved and it is seen that this game exhibits a surprising amount of unexplained regularity.
De Finetti Lattices and Magog Triangles
• Mathematics
Electron. J. Comb.
• 2021
The proof techniques are adopted to show that row reversal of an alternating sign matrix corresponds to a natural involution on gog triangles, and therefore is equinumerous with alternating sign matrices.

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