Timeline for Birkhoff's representation theorem vs matroid-geometric lattice correspondence
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Jul 17, 2022 at 0:54 | vote | accept | Igor Makhlin | ||
| Jul 17, 2022 at 0:54 | vote | accept | Igor Makhlin | ||
| Jul 17, 2022 at 0:54 | |||||
| Jul 16, 2022 at 17:39 | comment | added | Richard Stanley | @imakhlin: concerning Theorems 5 and 6, that is why I said the results "are analogous to characterizing finite distributive lattices as a collection of sets closed under union and intersection." It's not the type of characterization you are looking for, but it shows a different way to extend Birkhoff's theorem on finite distributive lattices. | |
| Jul 16, 2022 at 17:37 | history | edited | Richard Stanley | CC BY-SA 4.0 |
misspelling corrected
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| Jul 16, 2022 at 13:18 | comment | added | Igor Makhlin | I also fixed the broken link, hope you don't mind. | |
| Jul 16, 2022 at 13:17 | history | edited | Igor Makhlin | CC BY-SA 4.0 |
Fixed broken link.
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| Jul 16, 2022 at 13:16 | comment | added | Igor Makhlin | Thank you, very informative! So for a join-distributive lattice the considered family of subsets is the set of feasible sets in an antimatroid and this is a generalization of Birkhoff's theorem. But for the two subclasses of modular lattices the results (Theorems 5 and 6) don't seem to consider any subsets of join-irreducibles but, rather, provide characterizations as lattices of submodules? Or am I not looking closely enough? | |
| Jul 16, 2022 at 9:12 | history | answered | Richard Stanley | CC BY-SA 4.0 |