The Face Lattice of the Irreducible-Ferrers Polytope Is a Product of Triangles
Year: 2026
Type: preprint
Abstract: For every integer d at least 3, this note proves that the irreducible-Ferrers polytope introduced by Beeloo-Sauerbier Couvée and Neri is combinatorially equivalent to a Cartesian product of d-2 triangles. The proof recovers the complete face lattice from their nonnegative affine-slice model and vertex-support classification. Consequences include simplicity, the exact number of facets, and the complete face enumerator. Status: Public Beta; internally verified candidate proof; external review pending.
Author: Carptopus
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204104754
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