Amin Bahmanian

collaborators

5 papers

math.CO2026

The Andersen-Hoffman Theorem for Equitable Rectangles

Amin Bahmanian, Anna Johnsen-Yu

More than forty years ago, Andersen and Hoffman independently proved that every symmetric Latin rectangle can be extended to a symmetric Latin square with prescribed diagonal entri…

math.CO2026

Embedding Equitable Rectangles

Amin Bahmanian, Anna Johnsen-Yu

Completing partial Latin squares is NP-complete. Ryser characterized precisely when an $r \times s$ Latin rectangle can be completed to an $n \times n$ Latin square. We extend this t…

math.CO2025

Ryser's Theorem for Simple Multi-Latin Rectangle

Amin Bahmanian

We prove a general result on completing objects similar to Latin rectangles in which the number of occurrences of each symbol is prescribed, each cell contains multiple symbols, an…

math.CO2025

Toward a Three-dimensional Counterpart of Cruse's Theorem

Amin Bahmanian

Completing partial latin squares is NP-complete. Motivated by Ryser's theorem for latin rectangles, in 1974, Cruse found conditions that ensure a partial symmetric latin square of…

math.CO2025

Ryser's Theorem for Symmetric $I ¨ $ -latin Squares

Amin Bahmanian, A. J. W. Hilton

Let $L$ be an $n \times n$ array whose top left $r \times r$ subarray is filled with $k$ different symbols, each occurring at most once in each row and at most once in each column. W…

The Andersen-Hoffman Theorem for Equitable Rectangles

Embedding Equitable Rectangles

Ryser's Theorem for Simple Multi-Latin Rectangle

Toward a Three-dimensional Counterpart of Cruse's Theorem

Ryser's Theorem for Symmetric I¨-latin Squares

Ryser's Theorem for Symmetric $I ¨ $ -latin Squares