Resolvable 4-GDDs of types 2^u for u ∈ {46, 94, 100, 118, 130, 202, 214}
Year: 2026
Type: preprint
Abstract: We construct resolvable group divisible designs with block size four and groups of size two, 4-RGDDs, of types 246, 294, 2100, 2118, 2130, 2202 and 2214, seven of the nine possible exceptions for type 2u listed by Wei and Ge (2017) and Miller, Valkov and Abel (2026); the list becomes {70, 82}. For type 246 we give three non-isomorphic designs, each given by ten base blocks under a group of order 90, regular on 90 of the 92 points, which is the full automorphism group. The other six come from Schuster and Ge's generalized frame construction with eight added points, from explicit 4-frames of types 365, 248, 365 481, 367, 3611 and 369 961 and two incomplete uniformly resolvable designs on 32 and 44 points with block sizes 2 and 4, a hole of size 8 and one holey class of pairs, with automorphism groups of orders 8 and 18. Each design is determined by data in this paper. Equivalently, 92, 188, 200, 236, 260, 404 and 428 golfers can play in groups of four for 30, 62, 66, 78, 86, 134 and 142 weeks, the maximum, without two golfers meeting twice; the schedules recorded by Miller, Valkov and Abel have one week fewer. Schuster and Ge's generalized frame construction cannot reach the two remaining orders, as every instance needs a 4-RGDD of type 24 or 210; and in a 4-RGDD of type 282 no group of automorphisms preserving a resolution has a proper normal subgroup of order 41.
Author: kai
Institutions: University of Michigan, Federalist Society
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7222869620
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