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Algebraic Combinatorics

Jgmoxness, CC BY-SA 4.0 <https://creativecommons.org/licenses/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.

Contacts

 
Photo of Axel Hultman

Axel Hultman

Professor
 
Photo of Jan Snellman

Jan Snellman

Associate Professor, Docent

Publications

2023

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

2022

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 (Article in journal)

2019

Nancy Abdallah, Mikael Hansson, Axel Hultman (2019) Topology of posets with special partial matchings Advances in Mathematics, Vol. 348, p. 255-276 (Article in journal) 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 (Article in journal) Continue to DOI

2018

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 (Article in journal) Continue to DOI

2016

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

2014

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

2012

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

Doctoral theses

Cover of publication 'Boolean complexes of involutions and smooth intervals in Coxeter groups'
Vincent Umutabazi (2022)
Boolean complexes of involutions and smooth intervals in Coxeter groups
Cover of publication 'Combinatorics and topology related to involutions in Coxeter groups'
Mikael Hansson (2018)
Combinatorics and topology related to involutions in Coxeter groups
Cover of publication ''
Jonna Gill (2013)
The k-assignment polytope, phylogenetic trees, and permutation patterns

Organisation

A tiling of the hyperbolic plane. CRED: By Claudio Rocchini - Own work, CC BY 2.5, https://commons.wikimedia.org/w/index.php?curid=1669501.

Algebra, Geometry and Discrete Mathematics (ALGD)

Our research focuses on a number of different subject areas such as algebra, geometry, topology, dynamic systems, combinatorics and graph theory. The division consists of about twenty teachers, researchers and doctoral students.
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Department of Mathematics (MAI)

The department conducts research in computational mathematics, mathematics and applied mathematics, mathematical statistics, and optimization. We provide courses to students in most degree programmes in mathematics, science and engineering.
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About LiU

Linköping University, LiU, offers innovative education and boundary-crossing research. The students are among the most desirable in the labour market and international rankings consistently place LiU as a leading global university.

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