2018/01/23 by Gary R. W. Greaves, Gary Greaves, Greaves, Gary +2
Decision Sciences · Engineering · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Optimal Experimental Design Methods #VLSI and FPGA Design Techniques #graph theory and CDMA systems #math.CO
paper · pdf · doi:10.48550/arxiv.1801.07516
19 pages
openalex publication_date 2018/01/23 · openalex created_date 2018/02/02 · arxiv created 2018/05/06 · arxiv updated 2018/05/08 · openalex updated_date 2026/07/28
We show that the Smith normal form of a skew-symmetric D-optimal design of order n≡ 2\pmod4 is determined by its order. Furthermore, we show that the Smith normal form of such a design can be written explicitly in terms of the order n, thereby proving a recent conjecture of Armario. We apply our result to show that certain D-optimal designs of order n≡ 2\pmod4 are not equivalent to any skew-symmetric D-optimal design. We also provide a correction to a result in the literature on the Smith normal form of D-optimal designs.