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Group divisible designs with block size four and type gum1—II

Forbes, A. D. (2019). Group divisible designs with block size four and type gum1—II. Journal of Combinatorial Designs, 27(5) pp. 311–349.

DOI (Digital Object Identifier) Link: https://doi.org/10.1002/jcd.21650
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Abstract

We show that the necessary conditions for the existence of group divisible designs with block size four (4‐GDDs) of type gum1 are sufficient for g ≡ 0 (mod h), h = 39, 51, 57,69, 87, 93, 111, 123 and 129, and for g = 13, 17, 19, 23, 25,29, 31 and 35. More generally, we show that for g ≡ 3 (mod 6), the possible exceptions occur only when u = 8, and there are no exceptions at all if g/3 has a divisor d>1 such that d ≡ 1 (mod 4) or d is a prime not greater than 43. Hence there are no exceptions when g ≡ 3 (mod 12). Consequently, we are able to extend the known spectrum for g ≡ 1 and 5 (mod 6). Also, we complete the spectrum for 4‐GDDs of type (3α)4(6α)1(3b)1.

Item Type: Journal Item
Copyright Holders: 2019 Wiley Periodicals, Inc.
ISSN: 1520-6610
Keywords: double group divisible design; 4‐GDD; group divisible design
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
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Item ID: 59083
SWORD Depositor: Jisc Publications-Router
Depositing User: Jisc Publications-Router
Date Deposited: 11 Feb 2019 10:35
Last Modified: 29 Mar 2019 11:32
URI: http://oro.open.ac.uk/id/eprint/59083
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