Exact Dyadic Valuations for Step-Diagonal Domino Constraints
Required, forbidden, and mixed constraints on even square boards
Analyzes the exact power of two in matching counts under required, forbidden, or mixed step-diagonal constraints. A binary inverse-kernel calculation links local constraints to principal-minor valuations.
- Identifier
- MF-PRISM-MATH-2026-15
- Series
- Mathematics
- Edition
- Version 1.1
- Length
- 13 pages
- Reserved DOI
- 10.5281/zenodo.22728340 (record reserved)
What is this paper trying to establish?
What exact power of two divides domino-tiling counts under step-diagonal constraints?
The central idea.
Analyzes the exact power of two in matching counts under required, forbidden, or mixed step-diagonal constraints. A binary inverse-kernel calculation links local constraints to principal-minor valuations.
Candidate exact-valuation theorem; the separate odd-square refinement is not claimed.
This manuscript presents a candidate resolution. Publication is not verification: independent specialist review remains necessary before the result should be treated as established.
What changes if the method holds?
Exact valuations expose arithmetic structure that ordinary enumeration misses and distinguish the proved even-square theorem from an unproved odd-square refinement.
Where scrutiny should concentrate.
The paper identifies the following points as the highest-value targets for independent review.
- 01Binary kernel bases, first-order lifting, and the special boundary basis vector.
- 02Exact inverse residue and principal-minor valuations.
- 03Inclusion–exclusion for mixed constraints without importing the unproved odd-square refinement.
An open, inspectable research artifact.
The public record links the manuscript to its release, source package, review materials, and persistent identifier. Status travels with the paper; a reserved DOI is not presented as a published Zenodo record.
- Document
- Preprint
- Review status
- Open for independent review
- Published
- 2026-09-12
- DOI status
- Reserved · 10.5281/zenodo.22728340
- Canonical record
- MF-PRISM-MATH-2026-15