Parallel-Class Splitting and Constructive Lower Bounds for the Social Golfer Problem
Guido Witt-Dörring · Zenodo (CERN European Organization for Nuclear Research) · 2026
We establish constructive lower bounds for the Social Golfer Problem using resolvable designs and explicit schedules. We show that, for p≥2, any index-one RTD(p,2p-1) can have one parallel class replaced by two compatible classes, yielding W(2p-1,p)≥2p. In particular, this holds whenever 2p-1 is a prime power. Given an RTD(p,2p), the same replacement works when the number of groups is g=2p, although the resulting lower bound already follows from standard group filling. We also derive a ten-round schedule for groups of five on 50 players by completing a partial class of Brouwer's ITD(10,2;6) with two hole transversals. Finally, cyclic difference arrays or complete schedules establish W(20,7)≥15, W(21,7)≥16, W(28,7)≥21, and W(14,13)≥6. No exactness or optimality claim is made. The record includes the manuscript, LaTeX source, and supplementary schedules with a standalone Python validator. AI assistance in the research and manuscript drafting is disclosed in the paper. Licenses: the manuscript, LaTeX sources, schedules and original numerical tables are CC BY 4.0. The supplementary Python validator is MIT. These licenses apply to separate components; see LICENSES.txt.