Publications by Peter Dobcsányi

List of titles

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


Abstracts and Preprints

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: A Form Manager for the Class Language
Author(s): P. Dobcsányi, J. Hamer, J. G. Hosking
Status: published as Technical Report No.15, Department of Computer Science, University of Auckland, BRANZ Contract No.85-024, November 1990.


Title: DRL - a structured language for statistical data revision
Author(s): Peter Dobcsányi
Status: published as Reference Manual, Central Statistical Bureau, Hungary, 1988.