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๊ญ“le Ormsby ๐“†™
@e-infinity.space

I just analyzed 1.9M recipes and can now report that the yummy simplicial complex is arguably *not* flag. The following flavor trios have far fewer recipes containing all three ingredients than the recipes with pairs of ingredients would predict.

๊ญ“le Ormsby ๐“†™@e-infinity.space

An open problem in culinary mathematics: Consider the ๐‘ฆ๐‘ข๐‘š๐‘š๐‘ฆ ๐‘ ๐‘–๐‘š๐‘๐‘™๐‘–๐‘๐‘–๐‘Ž๐‘™ ๐‘๐‘œ๐‘š๐‘๐‘™๐‘’๐‘ฅ Y on vertex set I = {ingredients} where ฯƒโˆˆY iff the ingredients in ฯƒ appear in a single good recipe. Question: Is Y a flag simplicial complex? (A complex Y is ๐‘“๐‘™๐‘Ž๐‘” when ฯƒโˆˆY iff {x,y}โˆˆY for all x,yโˆˆฯƒ.)

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๊ญ“le Ormsby ๐“†™
@e-infinity.space

For me, the most compelling open triangle is tomato / lime / cottage cheese. tomato + lime = salsa tomato + cottage cheese = budget Caprese salad lime + cottage cheese = Grandma's lime jello salad tomato + lime + cottage cheese: get the fuck out of here.

Daniel McLaury
@danielmclaury.bsky.social

I didn't think you can just count recipes like that and have it mean anything. For one thing, 100 variants of basically the same recipe with slightly different ratios may not mean "these ingredients go well together." It may mean "you have to be really precise with the ratio here or it's bad"

๊ญ“le Ormsby ๐“†™
@e-infinity.space

I did some de-duplication and it decreased the number of recipes by 4%. I also did some cleaning so that, e.g., cream and sour cream are different ingredients. Overall structure didnโ€™t change much!