Further Results on the Construction of Mutually Orthogonal Latin Squares and the Falsity of Euler's Conjecture

1960/01/01 by R. C. Bose, S. S. Shrikhande, E. T. Parker · 6 citations
Decision Sciences · Engineering · Mathematics · #Combinatorics #Conjecture #Discrete mathematics #Euler's formula #Falsity #Function (biology) #Integer (computer science) #Latin square #Mathematical analysis #Mathematics #Mathematics and Applications #Optimal Experimental Design Methods #Order (exchange) #Prime (order theory) #Prime power #graph theory and CDMA systems

paper · pdf · doi:10.4153/cjm-1960-016-5

openalex publication_date 1960/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

If is the prime power decomposition of an integer v , and we define the arithmetic function n(v) by then it is known, MacNeish (10) and Mann (11), that there exists a set of at least n(v) mutually orthogonal Latin squares (m.o.l.s.) of order v . We shall denote by N(v) the maximum possible number of mutually orthogonal Latin squares of order v . Then the Mann-MacNeish theorem can be stated as MacNeish conjectured that the actual value of N(v) is n(v).

Citations

• ON THE FALSITY OF EULER'S CONJECTURE ABOUT THE NON-EXISTENCE OF TWO ORTHOGONAL LATIN SQUARES OF ORDER 4t + 2
• Orthogonal Arrays of Index Unity

Cited by

• Improving SAT Solvers on Orthogonal Latin Square Problems
• Max-Flow Min-Cut Theorems for Multi-User Communication Networks
• Masking quantum information in multipartite scenario
• Small latin squares, quasigroups, and loops
• Euler and combinatorial calculus
• Mutually orthogonal Latin squares [wikipedia]