Conjecture on Descents, Inversions and the Weak Order in Coxeter Systems

Explore a mathematical lecture examining partitions of elements in Coxeter systems, presented at the Workshop on "Recent Perspectives on Non-crossing Partitions through Algebra, Combinatorics, and Probability" at ESI. Delve into the relationship between left descents of partitioned elements and their connection to weak order in Coxeter systems, while investigating an intriguing conjecture that proposes the number of right descents in an element equals the sum of descent numbers within its partition. Learn how these mathematical concepts interweave through a detailed 37-minute presentation that advances understanding of algebraic combinatorics and partition theory.