Timeline for Cataland: Facets and partition polynomials of cluster complexes
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 12, 2023 at 21:55 | comment | added | Tom Copeland | See my answer mathoverflow.net/questions/441724/… for some more notes on the differences for m positive and m negative. | |
| Aug 12, 2023 at 21:48 | comment | added | Tom Copeland | Got bored with writing up some details of some proofs, came back to this question as a respite, and noticed the nodes at the three levels sum, starting from the top, to 14, 21, and 9, which are the number of vertices, edges, and facets of the 3-D associahedra, respectively. The refined face numbers of the associahedra are intimately related to the noncrossing partitions, which, in turn, are intimately related to refined (m)-Narayana / (m)-noncrossing partitions numbers for m a positive integer. My question addresses m for negative numbers (e.g., m=-2 in comment above). | |
| Apr 18, 2023 at 20:10 | comment | added | Tom Copeland | Nice app, I rarely do coding anymore, so thanks. Nathan Williams sent me an email giving the face vectors (7, 6, 1) and (30,36,12,1), which in my terminology correlates with $N^{(-2)}_3 = 7 u_1^3 - 6 u_2 u_1 + u_3$ and $N^{(-2)}_4 = -30 u_1^4 + 36 u_2 u_1^2 - 8 u_3 u_1 - 4 u_2^2 + u_4$. You'll find (7,6,1) in Armstrong on p. 144. | |
| Apr 18, 2023 at 12:54 | history | answered | Sam Hopkins | CC BY-SA 4.0 |