4 citations · 8 across the 6 of their papers we have counts for
11 papers · 1 filter
Crystal Pop-Stack Sorting and Type A Crystal Lattices
Colin Defant, Nathan Williams
Given a complex simple Lie algebra and a dominant weight , let be the crystal poset associated to the irreducible representation of wi…
Coxeter Pop-Tsack Torsing
Colin Defant, Nathan Williams
Given a finite irreducible Coxeter group with a fixed Coxeter element , we define the Coxeter pop-tsack torsing operator by $\mathsf{Pop}_T(w)=w\cdot…
Bijecting hidden symmetries for skew staircase shapes
Zachary Hamaker, Alejandro H. Morales, Igor Pak +2
We present a bijection between the set of standard Young tableaux of staircase minus rectangle shape, and the set of marked shifted standard Young tableaux of a certain shifted sha…
Normal Reflection Subgroups
Carlos E. Arreche, Nathan Williams
We study normal reflection subgroups of complex reflection groups. Our point of view leads to a refinement of a theorem of Orlik and Solomon to the effect that the generating funct…
Reflexponents
Nathan Williams
Certain classical generating functions for elements of reflection groups can be expressed using fundamental invariants called exponents. We give new analogues of such generating fu…
Strange Expectations and the Winnie-the-Pooh Problem
Marko Thiel, Nathan Williams
Motivated by the study of simultaneous cores, we give three proofs (in varying levels of generality) for the expected norm of a weight in a highest weight representation of a compl…