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Now showing items 1-10 of 16

#### On the table of marks of a direct product of finite groups

(Elsevier, 2017-12-28)

We present a method for computing the table of marks of a direct product of finite groups. In contrast to the character table of a direct product of two finite groups, its table of marks is not simply the Kronecker product ...

#### An algorithm for the unit group of the Burnside ring of a finite group

(Cambridge University Press, 2007-01)

In this note we present an algorithm for the construction of the unit group of
the Burnside ring Ω(G) of a finite group G from a list of representatives of the
conjugacy classes of subgroups of G.

#### A note on element centralizers in finite Coxeter groups

(De Gruyter, 2011-08-29)

The normalizer N-W(W-J) of a standard parabolic subgroup W-J of a finite Coxeter group W splits over the parabolic subgroup with complement N-J consisting of certain minimal length coset representatives of W-J in W. In ...

#### Computing the table of marks of a cyclic extension

(American Mathematical Society, 2012-02-24)

The subgroup pattern of a finite group C is the table of marks of G together with a list of representatives of the conjugacy classes of subgroups of G. In this article we present an algorithm for the computation of the ...

#### Computations for Coxeter arrangements and Solomon's descent algebra III: Groups of rank seven and eight

(Elsevier, 2014-11-06)

In this paper we extend the computations in parts I and II of this series of papers and complete the proof of a conjecture of Lehrer and Solomon expressing the character of a finite Coxeter group W acting on the p-th graded ...

#### Computations for Coxeter arrangements and Solomon's descent algebra II: Groups of rank five and six

(Elsevier, 2013-01-08)

In recent papers we have refined a conjecture of Lehrer and Solomon expressing the character of a finite Coxeter group W acting on the graded components of its Orlik-Solomon algebra as a sum of characters induced from ...

#### On the complexity of multiplication in the Iwahori-Hecke algebra of the symmetric group

(Elsevier, 2016-09-12)

We present new efficient data structures for elements of Coxeter groups of type Am and their associated Iwahori Hecke algebras H(A(m)). Usually, elements of H(A(m)) are represented as simple coefficient list of length M = ...

#### An inductive approach to Coxeter arrangements and Solomon's descent algebra

(Springer Verlag, 2012-07-20)

In our recent paper (Douglass et al. arXiv: 1101.2075 (2011)), we claimed that both the group algebra of a finite Coxeter group W as well as the Orlik-Solomon algebra of W can be decomposed into a sum of induced one-dimensional ...

#### Cohomology of Coxeter arrangements and Solomon's descent algebra

(American Mathematical Society, 2014-06-19)

We refine a conjecture by Lehrer and Solomon on the structure of the Orlik-Solomon algebra of a finite Coxeter group W and relate it to the descent algebra of W. As a result, we claim that both the group algebra of W and ...

#### Computations for Coxeter arrangements and Solomon's descent algebra: Groups of rank three and four

(Elsevier, 2012-06-03)

In recent papers we have refined a conjecture of Lehrer and Solomon expressing the characters of a finite Coxeter group W afforded by the homogeneous components of its Orlik-Solomon algebra as sums of characters induced ...