PermutahedronVertex

The vertex (σ(1), …, σ(n)), or its Loday point, is an ordered tuple of coordinates, while finset is an unordered set of positions (the carrier DescentSet and PeakSet use). Reordering the coordinates gives a different vertex but the same finset, so the map would not be injective. A finset-valued PermutahedronVertex is a type mismatch, not a gap to close. Not yet defined.

PermutahedronVertex(Permutation)

Domain: Combinatorial maps

Details

• Would take a Permutation to a Finset.
• On the map frontier: The vertex (σ(1), …, σ(n)), or its Loday point, is an ordered tuple of coordinates, while finset is an unordered set of positions (the carrier DescentSet and PeakSet use). Reordering the coordinates gives a different vertex but the same finset, so the map would not be injective. A finset-valued PermutahedronVertex is a type mismatch, not a gap to close.
• Declared undefined for that reason.

Examples

Basic #

the one-line word $231$ — once there is a definition to evaluate

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