Click on a title to get the abstract and possibly a preprint of the corresponding article.

- Searching for Symmetry in LIP/MIP Problems (slides)
- On balanced incomplete-block designs with repeated blocks
- Applications and adaptations of the low index subgroups algorithm
- Designs on the Web
- The External Representation of Block Designs
- Normal subgroups of low index in the modular group and other Hecke groups
- Trivalent symmetric graphs on up to 768 vertices
- Determination of all regular maps of small genus
- Test by JANZOS of the Standard Model of Cosmic Ray Acceleration in the COMPTEL/ROSAT Supernova Remnant
- A Form Manager for the Class Language
- DRL - a structured language for statistical data revision

**Title:**
*
On balanced incomplete-block designs with repeated blocks
*

**Author(s):**P. Dobcsányi, D. A. Preece and L. H. Soicher

**Status:** European Journal of Combinatorics 28 (2007)

**Abstract: **
Balanced incomplete-block designs (BIBDs) with repeated blocks are
studied and constructed. We continue work initiated by van Lint and
Ryser in 1972 and pursued by van Lint in 1973. We concentrate on
constructing (v,b,r,k,lambda)-BIBDs with repeated blocks, especially
those with gcd(b,r,lambda)=1 and r<=20. We obtain new
bounds for the multiplicity of a block in terms of the parameters of a
BIBD, and improvements to these bounds for a resolvable BIBD. This
allows us to answer a question of van Lint about the sufficiency of
certain conditions for the existence of a BIBD with repeated blocks.

**Download: ** repeated.pdf

**Title:**
*
Applications and adaptations of the low index subgroups procedure
*

**Author(s):** Marston Conder and Peter Dobcsányi

**Status:** Mathematics of Computation, 74 (2005), 485-497

**Math Review Classification(s): ** 20F05

**Abstract: **
The low-index subgroups procedure is an algorithm for finding all
subgroups of up to a given index in a finitely-presented group G, and
hence to determine all transitive permutation representations of G of
small degree. A number of significant applications of this algorithm are
discussed, in particular to the construction of graphs and surfaces with
large automorphism groups. Further, three useful adaptations of the
procedure are described, along with parallelisation of the algorithm.
In particular, one adaptation finds all complements of a given subgroup
of finite index, and another finds all normal subgroups of small index
in the group G. Significant recent applications of these are also
described in some detail.

**Download: ** lowindex.pdf

**Title:**
*
Designs on the Web
*

**Author(s):** R. A. Bailey, Peter J. Cameron, Peter
Dobcsányi, John P. Morgan, Leonard H. Soicher

**Status:** Discrete Mathematics 306, 2006.

**Abstract: **
In 2001, the United Kingdom Engineering and Physical Sciences Research
Council awarded three of the authors of this paper a grant for ``A
Web-based resource for design theory''. As the project developed, we
have had to face a number of problems, ranging from fundamental
questions such as ``What is a design?'', through research topics such as
``How should the concept of partial balance be extended to designs which
do not have constant block size?'', to more practical problems
concerning what format we should use to store designs. This paper gives
a brief description of the project to date, concentrating on theoretical
questions about designs and their classification.

**Download: ** designs-web.pdf

**Title:**
*
The External Representation of Block Designs v1.1
*

**Author(s):** Peter J. Cameron, Peter Dobcsányi,
John P. Morgan, Leonard H. Soicher

**Status:** Published online at
DesignTheory.org

**Description: **
This document should be of interest to those working in combinatorial
or statistical design theory, as well as those interested in the
development of standard electronic formats for mathematical objects.
We at DesignTheory.org are in the process of developing a web-based
Design Theory Resource Server for combinatorial and statistical design
theory. One critical element is our External Representation of Designs
which will be used to store designs and their combinatorial, group
theoretical and statistical properties in a standard
platform-independent manner. This will allow for the straightforward
exchange of designs and their properties between various computer
systems, including databases and web servers, and combinatorial, group
theoretical and statistical packages. The external representation will
also be used for outside submissions to our design database.

**Downloads:**
PDF
or
HTML

**Title:**
*
Normal subgroups of low index in the modular group and other Hecke groups
*

**Author(s):** Marston Conder and Peter Dobcsányi

**Status:** University of Auckland Mathematics
Department Research Report Series, No. 496, 23 pp, 2003.

**Math Review Classification(s): ** 20F05

**Abstract: **
An account is given of the determination of all normal subgroups
of index up to 1500 in the modular group PSL(2,Z) \cong C2*C3,
and all normal subgroups of index up to 500 in the Hecke groups
Hq = C2*Cq for 4 <= q <= 12, using an
adaptation of the low-index subgroups algorithm.

**Download: ** hecke.pdf

**Title:**
*
Trivalent symmetric graphs on up to 768 vertices
*

**Author(s):** Marston Conder and Peter Dobcsányi

**Status:** Journal of Combinatorial
Mathematics & Combinatorial Computing, 40 (2002), 41-63

**Math Review Classification(s): ** 05C25, 20B25, 20F05

**Abstract: **
A complete list is given of all finite trivalent arc-transitive connected
graphs on up to 768 vertices, completing and extending the Foster census.
Several previously undiscovered graphs appear, including one
on 448 vertices which is the smallest trivalent arc-transitive
graph having no automorphism of order 2 which reverses an arc.
The graphs on the list are classified according to type (as described
by Djokovic and Miller in terms of group amalgams), and were produced
with the help of a parallel program which finds all normal subgroups of low
index in a finitely-presented group. Further properties of each graph are
also given: its girth, diameter, Hamiltonicity, and whether or not it is
bipartite.

**Download: ** cubic768.pdf

**Title:**
*
Determination of all regular maps of small genus
*

**Author(s):** Marston Conder and Peter Dobcsányi

**Status:** The Journal of Combinatorial
Theory, Series B 81 (2001), 224-242

**Math Review Classification(s): ** 05C25, 57M15

**Abstract: **
Complete lists are given of all reflexible orientable regular maps of
genus 2 to 15, all non-orientable regular maps of genus 4 to 30,
and all (orientable) rotary but chiral (irreflexible) maps of genus
2 to 15 inclusive.
On each list the maps are classified according to genus and type
(viz. {p,q} where every face is incident with p edges and every
vertex is incident with q edges). The complete lists were determined
with the help of a parallel program which finds all normal subgroups of low
index in a finitely-presented group.

**Download: ** regmaps.pdf

**Title:**
*
Test by JANZOS of the Standard Model of Cosmic Ray Acceleration in the
COMPTEL/ROSAT Supernova Remnant
*

**Author(s):**
F. Abe, ... P. Dobcsányi, ... P. Yock, ... Y. Watase

**Status:** published in Proceedings of 26th Int Conf on Cosmic Rays (Utah)
Vol4, pp28-31 (1999)

**Abstract: **
A search for ultra-high energy gamma-rays emitted by the young, nerby
supernova remnant that was discovered by the COMPTEL and ROSAT
satellites was made using the JANZOS database for the period 1987-1993.
A 95% confidence upper limit on the flux above 100 TeV of 3x10^(-13)
cm^(-2)sec^(-1) was obtained. This is an order of magnitude below the
expected flux based on the standard model of cosmic ray acceleration in
supernove shocks.

**Download: ** janczos.pdf

**Title: **
* DRL - a structured language for statistical data revision *

**Author(s):** Peter Dobcsányi

**Status**: published as Reference Manual, Central Statistical Bureau,
Hungary, 1988.