... Hopf algebras in the graded case. In
order to study tame basic Hopf algebras or generally tame Hopf algebras, we
need more examples of tame Hopf algebras.
The Andruskiewitsch-Schneider algebra is ... modules for the quantum double of
a special Taft algebra in [3]. From this, we can deduce immediately that the
quantum double of this special Taft algebra is ta...
... rows and
columns of the adjacency matrix of G it is a block diagonal matrix in which every block
is an all-1 square matrix, and as our graph G has no loops, this means that it is a union
of complete ... a square all-1 matrix.
Proof of Theorem 1.1: The square of the number of perfect matchings of G counts
ordered pairs of such matchings. We claim that this is the...
... itself
a right translation of S if (ab)ρ = a( bρ) for all a, b ∈ S. A left translation λ and
a right translation ρ of S are said to be linked if a( λb)= (a )b for all a, b ∈ S.
In this case, we call ... translational hull of a type -A semigroup
is still of the same type [6], it is natural to ask whether the translational hull
of C-Ehresmann semigroups and their gene...
... Szemer´edi made a
breakthrough in this area when they provided a polynomial algorithm to find an
independent set of size at least
α(G) ≥
n log d
100d
.
* Correspondence to Tristan Denley, Matematiska institutionen, ... are designed to deal with the case when the average
degree of the graph is large. We shall prove that an r-regular graph without 3 and
5 cycles has an independence num...
... ≥
√
n
¯
d2 as claimed.
This improves Denley’s Theorems 1 and 2. It is sharp for the regular complete
bipartite graphs K
aa
.
The above results are readily extended to graphs of larger odd girth.
Lemma ... to
n.LetA (respectively B) be the set of vertices v of G such that the minimum label on
vertices at distance k or less from v is at even (respectively odd) distance k − 1orless.
It...
... partitions with unequal block
sizes
A. Knopfmacher
Department of Computational and Applied Mathematics
University of Witwatersrand
Johannesburg, South Africa
e-mail: arnoldk@gauss.cam.wits.ac.za
A. ... Stark
2
Department of Mathematics and Statistics
University of Melbourne
Parkville, Victoria 3052, Australia
e-mail: dstark@maths.mu.oz.au
G. Szekeres
Department of Mathematics
Univ...