Journal of Algebraic Combinatorics
1572-9192
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The Subconstituent Algebra of an Association Scheme (Part III)
Tập 2 Số 2 - Trang 177-210 - 1993
This is the continuation of an article from the previous issue. In this part, we
focus on the thin P- and Q-polynomial association schemes. We provide some
combinatorial characterizations of these objects and exhibit the known examples
with diameter at least 6. For each example, we give the irreducible modules for
the subconstituent algebra. We close with some conjectures and open problems.
Lattices of Parabolic Subgroups in Connection with Hyperplane Arrangements
Tập 9 Số 1 - Trang 5-24 - 1999
Let W be a Coxeter group acting as a matrix group by way of the dual of the
geometric representation. Let L be the lattice of intersections of all
reflecting hyperplanes associated with the reflections in this representation.
We show that L is isomorphic to the lattice consisting of all parabolic
subgroups of W. We use this correspondence to find all W for which L is
supersolvable. In particular, ...
On Elliptic Product Formulas for Jackson Integrals Associated with Reduced Root Systems
Tập 8 Số 2 - Trang 115-126 - 1998
In this note, we state certain product formulae for Jackson integrals associated
with any root systems, involved in elliptic theta functions which appear as
connection coefficients. The fomulae arise naturally in case of arbitrary root
systems by extending the connection problem which has been investigated in [1,
4] in case ofA type root system. This is also connected with the
Macdonald-Morris con...
Commutativity of association schemes of prime square order having non-trivial thin closed subsets
- 2008
Through a study of the structure of the modular adjacency algebra over a field
of positive characteristic p for a scheme of prime order p and utilizing the
fact that every scheme of prime order is commutative, we show that every
association scheme of prime square order having a non-trivial thin closed subset
is commutative.
An Essay on the Ree Octagons
Tập 4 Số 2 - Trang 145-164 - 1995
We coordinatize the Moufang generalized octagons arising from the Ree groups of
type 2 F 4. In this way, we obtain a very concrete and explicit description of
these octagons. We use this to prove some results on suboctagons, generalized
homologies, Suzuki-Tits ovoids and groups of projectivities of the Ree octagons.
All our results hold for arbitrary Ree octagons, finite or not.
Graphs with four distinct Laplacian eigenvalues
Tập 34 Số 4 - Trang 671-682 - 2011
In this paper, we investigate connected nonregular graphs with four distinct
Laplacian eigenvalues. We characterize all such graphs which are bipartite or
have exactly one multiple Laplacian eigenvalue. Other examples of interest are
also presented.
Dynkin Diagram Classification of λ-Minuscule Bruhat Lattices and of d-Complete Posets
Tập 9 Số 1 - Trang 61-94 - 1999
d-Complete posets are defined to be posets which satisfy certain local
structural conditions. These posets play or conjecturally play several roles in
algebraic combinatorics related to the notions of shapes, shifted shapes, plane
partitions, and hook length posets. They also play several roles in Lie theory
and algebraic geometry related to λ-minuscule elements and Bruhat distributive
lattices fo...