Timeline for Cataland: Facets and partition polynomials of cluster complexes
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Apr 23, 2023 at 22:20 | comment | added | Tom Copeland | See also mathoverflow.net/questions/445388/… | |
| Apr 22, 2023 at 6:26 | history | edited | Harry Richman | CC BY-SA 4.0 |
fixed abbreviation "S & S" for Speyer and Sturmfels
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| Apr 18, 2023 at 12:54 | answer | added | Sam Hopkins | timeline score: 1 | |
| Apr 18, 2023 at 11:32 | history | edited | Tom Copeland | CC BY-SA 4.0 |
Answer via email mentioned
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| Apr 15, 2023 at 4:32 | comment | added | Tom Copeland | Perhaps these two papers more directly address my concerns: "Rational associahedra and noncrossing partitions" by Armstrong, Rhoades, and Williams and "Rational parking functions and Catalan numbers" by Armstrong, Loehr, and Warrington. | |
| Apr 12, 2023 at 13:32 | comment | added | Tom Copeland | See also p. 121 of Nathan Williams' thesis "Cataland" (conservancy.umn.edu/handle/11299/159973). | |
| Apr 7, 2023 at 16:07 | history | edited | Tom Copeland | CC BY-SA 4.0 |
minor edits
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| Apr 7, 2023 at 5:22 | history | edited | Tom Copeland | CC BY-SA 4.0 |
Elaborated on similar models
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| Apr 6, 2023 at 3:17 | history | edited | Tom Copeland | CC BY-SA 4.0 |
Further addressed Sam's comments
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| Apr 5, 2023 at 21:52 | comment | added | Tom Copeland | @SamHopkins, I'm looking for the busy crossroads rather than quiet alleys, and yes it is much more difficult to associate the ParPs for the comp. inverse of e.g.f.s with Grassmannian simplicial complexes (not convex polytopes)--that hasn't stopped Thron, Price, Getzler, Cachazo from doing so or forming more complicated links between alg. and geom. comb. The associahedra and noncrossing ParPs (not polytopes) have been linked with more complex analytics and QFT. The m-associahedra and m-noncrossing partitions are related to Feynman diagrams as well. Algebra and geometry inform each other. | |
| Apr 5, 2023 at 21:24 | history | edited | Tom Copeland | CC BY-SA 4.0 |
Response to comment
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| Apr 5, 2023 at 20:51 | comment | added | Sam Hopkins | You don't actually need geometric pictures to capture the difference between e.g. square faces and hexagonal faces. A square face contains 4 vertices (& 4 edges), while a hexagonal face has 6. So this kind of information is captured by the "abstract" combinatorial structure of the polytope, in the sense of: en.wikipedia.org/wiki/Abstract_polytope | |
| Apr 5, 2023 at 20:46 | history | asked | Tom Copeland | CC BY-SA 4.0 |