A family of algebraic structures that some of us give a lot of attention is that of Coxeter groups. They appear, for example, in the study of symmetries; as special cases of Coxeter groups one finds the symmetries of the five platonic solids (as well as higher-dimensional regular polytopes). Other examples include the Weyl groups associated with root systems that are important in Lie theory and, consequently, in theoretical physics.
Algebraic Combinatorics
The practitioners of algebraic combinatorics are interested in combinatorial aspects of algebraic objects in order to explain, make concrete, and describe their properties. Sometimes the roles are reversed, with algebraic machinery providing insight into traditionally combinatorial domains.
Contacts
Publications
2026
Bounds for the entropy of graded algebras
Communications in Algebra
(Article in journal)
https://dx.doi.org/10.1080/00927872.2026.2665319
2025
The Multi-Generating Function for Intervals in Young's Lattice: some Comments on a Paper by Azam and Richmond
The Electronic Journal of Combinatorics, Vol. 32, Article 49
(Article in journal)
https://dx.doi.org/10.37236/13847
2023
Boolean Complexes of Involutions
Annals of Combinatorics, Vol. 27, p. 129-147
(Article in journal)
https://dx.doi.org/10.1007/s00026-022-00629-9
2022
Smoothness of Schubert varieties indexed by involutions in finite simply laced types
Seminaire Lotharingien de Combinatoire, Vol. 84, Article B84b
(Article in journal)
2019
Topology of posets with special partial matchings
Advances in Mathematics, Vol. 348, p. 255-276
(Article in journal)
https://dx.doi.org/10.1016/j.aim.2019.02.031
A word property for twisted involutions in Coxeter groups
Journal of combinatorial theory. Series A (Print), Vol. 161, p. 220-235
(Article in journal)
https://dx.doi.org/10.1016/j.jcta.2018.07.006
2018
Combinatorial invariance of Kazhdan-Lusztig-Vogan polynomials for fixed point free involutions
Journal of Algebraic Combinatorics, Vol. 47, p. 543-560
(Article in journal)
https://dx.doi.org/10.1007/s10801-017-0785-z
2016
Supersolvability and the Koszul property of root ideal arrangements
Proceedings of the American Mathematical Society, Vol. 144, p. 1401-1413
(Article in journal)
https://dx.doi.org/10.1090/proc/12810
