A conjecture on descents, inversions and the weak order

Viviane Pons (Paris-Saclay U)

Feb 19. 2025, 09:00 — 09:45

We discuss the notion of partitions of elements in an arbitrary Coxeter system: a partition of an element w is the set of elements such that the left descents of w are the disjoint union of the left descents of the elements in the partition. This is related to the weak order of a Coxeter system and leads to an interesting conjecture that the number of right descents in w is the sum of the numbers of descents in the partition.

Further Information
Venue:
ESI Boltzmann Lecture Hall
Recordings:
Recording
Files:
Slides
Associated Event:
Recent Perspectives on Non-crossing Partitions through Algebra, Combinatorics, and Probability (Workshop)
Organizer(s):
Adrian Celestino Rodriguez (TU Graz)
Kurusch Ebrahimi-Fard (NTNU, Trondheim)
James Mingo (Queen's U, Kingston)
Martin Rubey (TU Vienna)
Eleni Tzanaki (U of Crete)
Yannic Vargas (CUNEF U, Madrid)