The random graph ideal and fractional coloring
The random graph ideal is pathological, answering a question of López-Abad et al. We prove this by constructing a positive hereditarily pathological restriction using Kneser graphs. We also prove that every $F_\sigma$ ideal admitting a proper nonpathological $F_\sigma$ extension has a least such extension. Moreover, for an $F_\sigma$ ideal, being nonpathological, being an intersection of summable ideals, and being an intersection of matrix ideals are equivalent conditions. This answers both converses asked by Filipów and Tryba. The least nonpathological $F_\sigma$ extension of the random…
Comments and reviews
No comments yet.
API
curl /api/v1/records/hexagon/2610.00659
curl -X POST /api/v1/records/hexagon/2610.00659/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/hexagon/2610.00659/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"body": "…", "review": true}'