Contact coverage observability

Happy Diner Frontier

T(n,k) is the minimum number of sessions needed for every unordered pair among n people to share a group at least once when group occupancy is at most k; empty groups and varying occupancy are allowed.

artifact v2 · registry happy-diner-frontier-dagstuhl-tables-v2 · select or focus cells for exact evidence

primary cells210

dual coordinates341

dual reported238

dual ranges103

validated witnesses2

exactly certified36

bracketed1

lower-bound only173

center W validated GroupMixer witness upper boundcenter ≥L certified floor when no local witness is knowntop-right T Dagstuhl source value/rangebottom-left L centralized GroupMixer lower boundexactly certifiedcertified bracketwider certified bracketunresolved wide certified bracketlower bound only; deeper blue means a larger certified floorliterature only◆ source marks a perfect solution† source marks the value unverified

Complete pinned source

Dagstuhl T×k source atlas

n(T,k) is the maximum participant count reported possible with at most T sessions and group occupancy at most k; these are pinned Dagstuhl source claims, not GroupMixer certificates.

How to read it: each cell is the source's reported maximum participant count n(T,k). A range preserves source uncertainty; ◆ marks a source-perfect solution; † marks the source's unverified J argument. Blank cells are intentional omissions in the upstream table and are not inferred here.

341coordinates238reported135exact values103ranges52perfect20unverified J103intentional blanks

Complete pinned Dagstuhl inverse table: sessions T by capacity k, with participant-count values or ranges.
T \ k	2	3	4	5	6	7	8	9	10	11	12
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Local refinement layer

GroupMixer certified n×k frontier

Rows are participant count n; columns are maximum group occupancy k. Select a cell for proof and provenance details; arrow keys move between cells.

Refinement scope: this layer overlays centralized GroupMixer lower bounds and validated witnesses on Dagstuhl's rectangular primary table. The complete pinned dual source table is preserved above without promoting its claims to local certificates.

n \ k	2	3	4	5	6	7	8
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Method reference

label	meaning
`DAG`	Validated schedule imported from Dagstuhl-tables
`TRIV`	Trivial one-session construction for n ≤ k (or zero sessions for n=1)

Source and evidence policy

Source-table values are reference claims. Only centralized GroupMixer bounds and locally validated schedules are displayed as GroupMixer certificates.

key	citation	source	commit	notes
`dagstuhl-tables`	Floris van Doorn, Auke Booij, and contributors. Dagstuhl's Happy Diner Problem tables and explicit schedules.	Dagstuhl-tables	`5b7b244a94cc`	Primary and dual tables transcribed mechanically; selected explicit schedules parsed and pair-coverage validated locally.