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RUP
FAMNIT - Faculty of Mathematics, Science and Information Technologies
FHŠ - Faculty of Humanities
FM - Faculty of Management
FTŠ Turistica - Turistica – College of Tourism Portorož
FVZ - Faculty of Health Sciences
IAM - Andrej Marušič Institute
PEF - Faculty of Education
UPR - University of Primorska
ZUP - University of Primorska Press
COBISS
University of Primorska, University Library - all departments
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Title:
Leonard triples and hypercubes
Authors:
ID
Miklavič, Štefko
(Author)
Files:
http://dx.doi.org/10.1007/s10801-007-0108-x
Language:
English
Work type:
Not categorized
Typology:
1.01 - Original Scientific Article
Organization:
IAM - Andrej Marušič Institute
Abstract:
Let
V
denote a vector space over
C
with finite positive dimension. By a Leonard triple on
V
we mean an ordered triple of linear operators on
V
such that for each of these operators there exists a basis of
V
with respect to which the matrix representing that operator is diagonal and the matrices representing the other two operators are irreducible tridiagonal. Let
D
denote a positive integer and let
Q
D
denote the graph of the
D
-dimensional hypercube. Let
X
$
d
e
n
o
t
e
t
h
e
v
e
r
t
e
x
s
e
t
o
f
▫
$
Q
D
and let
A
∈
M
a
t
X
(
C
)
denote the adjacency matrix of
Q
D
. Fix
x
∈
X
and let
A
∗
∈
M
a
t
X
(
C
)
denote the corresponding dual adjacency matrix. Let
T
denote the subalgebra of
M
a
t
X
(
C
)
$
g
e
n
e
r
a
t
e
d
b
y
▫
$
A
,
A
∗
. We refer to
T
as the Terwilliger algebra of
Q
D
with respect to
x
. The matrices
A
and
A
∗
are related by the fact that
2
i
A
=
A
∗
A
ε
−
A
ε
A
∗
and
2
i
A
∗
=
A
ε
A
−
A
A
ε
, where
2
i
A
ε
=
A
A
∗
−
A
∗
A
and
i
2
=
−
1
. We show that the triple
A
,
A
∗
,
A
ε
acts on each irreducible
T
-module as a Leonard triple. We give a detailed description of these Leonard triples.
Keywords:
mathematics
,
graph theory
,
Leonard triple
,
distance-regular graph
,
hypercube
,
Terwilliger algebra
Year of publishing:
2007
Number of pages:
str. 397-424
Numbering:
Vol. 28, no. 3
PID:
20.500.12556/RUP-1597
ISSN:
0925-9899
UDC:
519.17
COBISS.SI-ID:
14624857
Publication date in RUP:
15.10.2013
Views:
5607
Downloads:
124
Metadata:
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:
MIKLAVIČ, Štefko, 2007, Leonard triples and hypercubes. [online]. 2007. Vol. 28, no. 3, p. 397–424. [Accessed 17 March 2025]. Retrieved from: http://dx.doi.org/10.1007/s10801-007-0108-x
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Secondary language
Language:
English
Keywords:
matematika
,
teorija grafov
,
razdaljno regularni grafi
,
Leonardova trojica
,
hiperkocka
,
Terwilligerjeva algebra
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