2016/02/02 by Yutaka Nishiyama, Nishiyama, Yutaka, Nozomi Miyanaga +1
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · #Cellular Automata and Applications #DNA and Biological Computing #FOS: Mathematics #History and Overview (math.HO) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1602.03736
openalex publication_date 2016/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper discusses a 100-cell calculation table for addition, C(i,j)=Ai+Bj,(1<=i,j<=10), addressing the special case where the 100 cells C(i,j) comprise continuous numbers 0 through 99. We consider what sequences Ai,Bj,(1<=i,j<=10) are needed to fulfill these conditions, and the number of possible combinations. We first find seven solutions through factorization of the generating function used for Sicherman dice. We next find seven solutions through geometric means. We demonstrate a correspondence between the seven solutions from factorization and the seven from geometry. Finally, we suggest that the number of solutions N for an nxn=n2-cell calculation table is N=(p-2)(p-1)+1, where p is the number of divisors of n.