Henri Mühle (TU Dresden)
TITLE: Refined Face Enumeration in v-Associahedra
ABSTRACT: Chapoton defined for each finite root system three remarkable polynomials, the F-, H- and M-triangle. \; The F-triangle is a refined face generating polynomial of the cluster complex, the H-triangle is a refined generating function of nonnesting partitions, and the M-triangle is a bivariate generating function of the Möbius function in the noncrossing partition lattice. \; He observed that these three polynomials are related by an invertible substitution of variables. \; These observations were proven uniformly by Athanasiadis and Thiel, respectively. \;
In this talk, we explain how the F- and the H-triangle arise as refined versions of the f- and the h-polynomial of a polytope, and give a simple, combinatorial proof of Chapoton's relation in the context of v-associahedra. \; The relation with the M-triangle is much less clear. \; We conjecture a characterization of the northeast paths for which Chapoton's relation generalizes to this setting. \; Computational evidence suggests a close connection to the pureness of v-associahedra. \;
This is based on joint work with Cesar Ceballos from TU Graz.
Where: Seminar Room @ Villa and Zoom:
https://sfsu.zoom.us/j/88391753769?pwd=OEpTVjBic2ZRZmw4UytIUmlOS3E0UT09
Meeting ID: 883 9175 3769
Passcode: 339409
Isabella Novik (University of Washington)
Where: Seminar Room @ Villa and Zoom:
https://sfsu.zoom.us/j/88391753769?pwd=OEpTVjBic2ZRZmw4UytIUmlOS3E0UT09
Meeting ID: 883 9175 3769
Passcode: 339409
Martina Junke-Kubitzke (U Osnabrück)
Where: Seminar Room @ Villa and Zoom:
https://sfsu.zoom.us/j/88391753769?pwd=OEpTVjBic2ZRZmw4UytIUmlOS3E0UT09
Meeting ID: 883 9175 3769
Passcode: 339409
Isabel Hubard (UNAM)
Where: Seminar Room @ Villa and Zoom:
https://sfsu.zoom.us/j/88391753769?pwd=OEpTVjBic2ZRZmw4UytIUmlOS3E0UT09
Meeting ID: 883 9175 3769
Passcode: 339409
Aram Dermenjian (York University)
Where: Seminar Room @ Villa and Zoom:
https://sfsu.zoom.us/j/88391753769?pwd=OEpTVjBic2ZRZmw4UytIUmlOS3E0UT09
Meeting ID: 883 9175 3769
Passcode: 339409
Julian Pfeifle (UPC Barcelona)
Where: Seminar Room @ Villa and Zoom:
https://sfsu.zoom.us/j/88391753769?pwd=OEpTVjBic2ZRZmw4UytIUmlOS3E0UT09
Meeting ID: 883 9175 3769
Passcode: 339409
Thomas Kahle (OvGU Magdeburg)
Where: Seminar Room @ Villa and Zoom:
https://sfsu.zoom.us/j/88391753769?pwd=OEpTVjBic2ZRZmw4UytIUmlOS3E0UT09
Meeting ID: 883 9175 3769
Passcode: 339409
Laith Rastanawi (FU Berlin)
Where: Seminar Room @ Villa and Zoom:
https://sfsu.zoom.us/j/88391753769?pwd=OEpTVjBic2ZRZmw4UytIUmlOS3E0UT09
Meeting ID: 883 9175 3769
Passcode: 339409