Timeline for How linearly independent are the obvious combinatorial invariants of a Bruhat interval?
Current License: CC BY-SA 2.5
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| Jul 21, 2010 at 22:30 | comment | added | Qiaochu Yuan | Thanks for the link! In the notation of that post, I am only looking for relations between the f_i and the f_{i,i+1}, and it doesn't look like the argument described gives many such relations. But I'll have to take a closer look at the Bayer-Billera relations. | |
| Jul 21, 2010 at 21:38 | comment | added | Richard Stanley | Since Bruhat intervals are Eulerian their flag $f$-vectors satisfy the Bayer-Billera relations. These give many relations of the type you are looking for. For instance, Gil Kalai gives a few examples at gilkalai.wordpress.com/2008/06/22/…. I doubt whether the flag $f$-vectors of Bruhat intervals satisfy any linear relations not already a consequence of the Eulerian property. | |
| Jul 21, 2010 at 20:38 | history | edited | Qiaochu Yuan | CC BY-SA 2.5 |
added 272 characters in body
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| Jul 21, 2010 at 20:22 | comment | added | Alexander Woo | Should we say that the functions you are interested in are all parts of the flag f-vector? Can we rephrase your question as: what are defining equations of the subspace of flag f-vectors spanned by Bruhat intervals? Maybe we can then pass to the right family polytopes to think about this? | |
| Jul 21, 2010 at 19:36 | history | asked | Qiaochu Yuan | CC BY-SA 2.5 |