# 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} }

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

- MathematicsInt. 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

- MathematicsIntegers
- 2018

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

- MathematicsElectron. 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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