On the Smith normal form of a skew-symmetric D-optimal design of order n≡2 (mod4)
We show that the Smith normal form of a skew‐symmetric D‐optimal design of order n≡2 (mod 4) 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 re...
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sg-ntu-dr.10356-1466702023-02-28T19:52:46Z On the Smith normal form of a skew-symmetric D-optimal design of order n≡2 (mod4) Greaves, Gary Royden Watson Suda, Sho School of Physical and Mathematical Sciences Science::Mathematics D‐optimal Design EW Tournament Matrix We show that the Smith normal form of a skew‐symmetric D‐optimal design of order n≡2 (mod 4) 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(mod 4)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. Ministry of Education (MOE) Accepted version Singapore Ministry of Education Academic Research Fund (Tier 1),Grant/Award Number: RG127/16; JSPS KAKENHI, Grant/Award Number: 15K21075 2021-03-04T07:51:45Z 2021-03-04T07:51:45Z 2018 Journal Article Greaves, G. R. W., & Suda, S. (2019). On the Smith normal form of a skew-symmetric D-optimal design of order n≡2 (mod4). Journal of Combinatorial Designs, 27(3), 123-141. doi:10.1002/jcd.21626 1063-8539 https://hdl.handle.net/10356/146670 10.1002/jcd.21626 3 27 123 141 en RG127/16 Journal of Combinatorial Designs This is the peer reviewed version of the following article: Greaves, G. R. W., & Suda, S. (2019). On the Smith normal form of a skew-symmetric D-optimal design of order n≡2 (mod4). Journal of Combinatorial Designs, 27(3), 123-141, which has been published in final form at https://doi.org/10.1002/jcd.21626. This article may be used for non-commercial purposes in accordance with the Wiley Terms and Conditions for Use of Self-Archived Versions. application/pdf |
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Science::Mathematics D‐optimal Design EW Tournament Matrix Greaves, Gary Royden Watson Suda, Sho On the Smith normal form of a skew-symmetric D-optimal design of order n≡2 (mod4) |
| description |
We show that the Smith normal form of a skew‐symmetric D‐optimal design of order n≡2 (mod 4) 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(mod 4)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. |
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School of Physical and Mathematical Sciences |
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School of Physical and Mathematical Sciences Greaves, Gary Royden Watson Suda, Sho |
| format |
Article |
| author |
Greaves, Gary Royden Watson Suda, Sho |
| author_sort |
Greaves, Gary Royden Watson |
| title |
On the Smith normal form of a skew-symmetric D-optimal design of order n≡2 (mod4) |
| title_short |
On the Smith normal form of a skew-symmetric D-optimal design of order n≡2 (mod4) |
| title_full |
On the Smith normal form of a skew-symmetric D-optimal design of order n≡2 (mod4) |
| title_fullStr |
On the Smith normal form of a skew-symmetric D-optimal design of order n≡2 (mod4) |
| title_full_unstemmed |
On the Smith normal form of a skew-symmetric D-optimal design of order n≡2 (mod4) |
| title_sort |
on the smith normal form of a skew-symmetric d-optimal design of order n≡2 (mod4) |
| publishDate |
2021 |
| url |
https://hdl.handle.net/10356/146670 |
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1759856683060822016 |