Algebraic Combinatorics

Jgmoxness, CC BY-SA 4.0 <>, via Wikimedia Commons

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.

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.




Axel Hultman, Vincent Umutabazi (2023) Boolean Complexes of Involutions Annals of Combinatorics, Vol. 27, p. 129-147 Continue to DOI


Axel Hultman, Vincent Umutabazi (2022) Smoothness of Schubert varieties indexed by involutions in finite simply laced types Seminaire Lotharingien de Combinatoire, Vol. 84, Article B84b


Nancy Abdallah, Mikael Hansson, Axel Hultman (2019) Topology of posets with special partial matchings Advances in Mathematics, Vol. 348, p. 255-276 Continue to DOI
Mikael Hansson, Axel Hultman (2019) A word property for twisted involutions in Coxeter groups Journal of combinatorial theory. Series A (Print), Vol. 161, p. 220-235 Continue to DOI


Nancy Abdallah, Axel Hultman (2018) Combinatorial invariance of Kazhdan-Lusztig-Vogan polynomials for fixed point free involutions Journal of Algebraic Combinatorics, Vol. 47, p. 543-560 Continue to DOI


Axel Hultman (2016) Supersolvability and the Koszul property of root ideal arrangements Proceedings of the American Mathematical Society, Vol. 144, p. 1401-1413 Continue to DOI


Axel Hultman (2014) Permutation statistics of products of random permutations Advances in Applied Mathematics, Vol. 54, p. 1-10 Continue to DOI


Axel Hultman (2012) Criteria for rational smoothness of some symmetric orbit closures Advances in Mathematics, Vol. 229, p. 183-200 Continue to DOI

Doctoral theses