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 v1 · registry happy-diner-frontier-dagstuhl-tables-v1 · select or focus cells for exact evidence

cells210

source exact201

source ranges6

source unverified3

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 the value unverified

Certified search space

Primary 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.

Source scope: this view mirrors Dagstuhl's 210-cell primary table. Its inverse T×k table reaches T=31, k=12, and participant ranges up to n=244; that broader projection is not included here yet.

n \ k	2	3	4	5	6	7	8
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30

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 table transcribed mechanically; selected explicit schedules parsed and pair-coverage validated locally.