Interior Multiples of the Latin Eulerian Total

Abstract

Every permitted interior multiple of the order occurs as the total column-ascent number of a Latin square.

Theorem 1.1 (Every interior multiple occurs).

$c l aim$

Proof. Machine-checked in Lean as D5/S3/Combinatorics/LatinEulerianMultiples.result (✓ std3). ∎

Resolves. Problems/mirzavaziri-yaqubi-latin-eulerian-multiples (proved) by D5/S3/Combinatorics/LatinEulerianMultiples.result.

Source. Repository-derived.

Acknowledgement. Madjid Mirzavaziri, Daniel Yaqubi (2026). Latin Eulerian Numbers. DOI: 10.48550/arXiv.2609.25100. URL: https://arxiv.org/abs/2609.25100v1.

Commentary.

For every n at least five and every k between two and n minus three, there is an order-n Latin square with total ascent number k n.