LatinTableau.lean`

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Project sources: Pinned project documentation, Formal Conjectures paper, arXiv v1

1 declarations, 1 contain sorry, 0 declared as axioms

Latin Tableau Conjecture

The Latin Tableau Conjecture states that the graph associated to any (finite) Young diagram (i.e., whose vertices are the cells of the diagram, with edges between cells in the same row or column) is CDS-colorable, meaning that there exists a proper coloring of the vertices of the graph such that for all k > 0, the number of vertices with color < k equals the maximum size of the union of k independent sets of the graph.

References:

The Latin Tableau Conjecture

Imports (1)

FormalConjecturesUtil

theorem LatinTableau.SimpleGraph.LatinTableauConjecture The Latin Tableau Conjecture: If G is the simple graph of a Young diagram, then G is CDS-colorable sorry line 47 source
Source documentation
The Latin Tableau Conjecture: If G is the simple graph of a Young diagram, then G is CDS-colorable.

depends on sorry what this means
Statement uses: YoungDiagram, SimpleGraph.CDSColorable, YoungDiagram.Cell, YoungDiagram.toSimpleGraph
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous, OfNat.ofNat, Nat
3 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem LatinTableauConjecture (μ : YoungDiagram) :
     μ.toSimpleGraph.CDSColorable := by sorry
```