Marston Conder

• Distinguished Professor of Mathematics (and former Co-Director of the New Zealand Institute of Mathematics and its Applications (the NZIMA))
  
• Email: m.conder@auckland.ac.nz
  
• Telephone: +64 9 9238879
  
• Fax: +64 9 3737457
  
• Office: Rm 417 SMIS/Physics building
  

Research interests

Publications

Lists of regular maps, hypermaps and polytopes, trivalent symmetric graphs, and surface actions

    Regular/chiral maps and hypermaps

• all regular orientable maps on surfaces of genus 2 to 101, up to isomorphism and duality, with defining relations for their automorphism groups
• all regular non-orientable maps on surfaces of genus 2 to 202, up to isomorphism and duality, with defining relations for their automorphism groups
• all chiral (irreflexible) orientably-regular maps on surfaces of genus 2 to 101, up to isomorphism, duality and reflection, with defining relations for their automorphism groups
• all proper orientable regular hypermaps on surfaces of genus 2 to 101, up to isomorphism and triality, with defining relations for their automorphism groups [WARNING: this is a 4.34MB file!]
• all proper non-orientable regular hypermaps on surfaces of genus 2 to 202, up to isomorphism and triality, with defining relations for their automorphism groups
• all proper chiral orientably-regular hypermaps on surfaces of genus 2 to 101, up to isomorphism, triality and reflection, with defining relations for their automorphism groups
• all regular orientable maps on surfaces of genus 2 to 301, up to isomorphism and duality, with defining relations for their automorphism groups
• all chiral (irreflexible) orientably-regular maps on surfaces of genus 2 to 301, up to isomorphism, duality and reflection, with defining relations for their automorphism groups
• all regular non-orientable maps of genus 2 to 602, up to isomorphism, duality and reflection, with defining relations for their automorphism groups
• all rotary maps on closed surfaces with up to 1000 edges, up to isomorphism and duality and other transformations (including Petrie duality and opposite, when the map is fully regular, and missor image when the map is chiral)
• all fully regular maps on closed surfaces with up to 1000 edges, up to isomorphism and transformation under the six "Wilson" operators (duality, Petrie duality, opposite, etc.)
• all chiral rotary maps on orientable surfaces with up to 1000 edges, up to isomorphism, mirror image and duality
• all orientably-regular maps with rotation group of order at most 400
• all orientably-regular maps with rotation group a non-dihedral group of order at most 400
• regular and orientably-regular maps on closed surfaces having small Euler characteristic, listed by their type, up to duality
• regular and orientably-regular maps on closed surfaces having small non-positive Euler characteristic, listed by their type, up to duality
• regular and orientably-regular maps on closed surfaces having small negative Euler characteristic, listed by their type, up to duality

    Group actions on surfaces

• all quotients of triangle groups that act on compact Riemann surfaces of genus 2 to 101, up to isomorphism, duality/triality and reflection, with defining relators (normal generators for the kernel) [WARNING: this is a 4.0MB file!]
• all large groups of automorphisms of compact Riemann surfaces of genus 2 to 101, up to equivalence of the group action, listed by the type of Fuchsian group (with triangular or quadrangular signature), along with defining relators (normal generators for the kernel) [WARNING: this is a 22.8MB file!]
• all large groups of automorphisms of compact Riemann surfaces of genus 2 to 101, up to equivalence of the group action, listed by genus, along with the type of Fuchsian group (with triangular or quadrangular signature), and group defining relators (normal generators for the kernel) [WARNING: this is a 25.6MB file!]
• a summary of the maximum orders of group actions on compact Riemann surfaces of genus 2 to 301, with signature types for the actions that have the maximum order
• a summary of the maximum orders of group actions on compact non-orientable Klein surfaces of genus 3 to 302, with signature types for the actions that have the maximum order
• a summary of the strong symmetric genus of all groups of order 2 to 127, including the signature types for the actions of the group on (orientable) surfaces of the corresponding genus
• a list of all the finite groups with strong symmetric genus 2 to 32, including the signature types for the actions of the group on (orientable) surfaces of the corresponding genus
• a summary of the symmetric genus of all groups of order 2 to 127, including the signature types for the actions of the group on (orientable) surfaces of the corresponding genus
• a list of all the finite groups with symmetric genus 2 to 32, including the signature types for the actions of the group on (orientable) surfaces of the corresponding genus
• a summary of the symmetric cross-cap number of all groups of order 2 to 127, including the signature types for the actions of the group on (non-orientable) surfaces of the corresponding genus
• a list of all the finite groups with symmetric cross-cap number 3 to 65, including the signature types for the actions of the group on (non-orientable) surfaces of the corresponding genus

    Symmetric graphs

• all trivalent (cubic) symmetric graphs on up to 2048 vertices, up to isomorphism, categorised by their type, and with a link to a 6.1Mb gzipped directory containing all the graphs themselves
• all trivalent (cubic) symmetric graphs on up to 10000 vertices, up to isomorphism, categorised by their type, etc., with this link to a 370.1Mb file containing the edge-sets, and this link to a 113.6Mb gzipped version of that file.
• all symmetric graphs of order 2 to 30, up to isomorphism, with some information about their automorphism groups.
• all symmetric graphs of order 2 to 47, up to isomorphism, and given by their edge-sets, with some information about their automorphism groups.
• all symmetric graphs of order 2 to 47, up to isomorphism, and given by the neighbours of each vertex, with some information about their automorphism groups.

    Semi-symmetric graphs

• summary of all trivalent (cubic) semi-symmetric graphs on up to 10000 vertices, up to isomorphism, listed by order, and then by Goldschmidt type.

    Regular/chiral polytopes

• all regular polytopes with up to 2000 flags, up to isomorphism and duality, ordered by the number of flags under each rank, excluding those of rank 2 (regular polygons) and the degenerate examples that have a '2' in their Schlaefli symbol
• all regular polytopes with up to 2000 flags, up to isomorphism and duality, ordered by their type under each rank, excluding those of rank 2 (regular polygons) and the degenerate examples that have a '2' in their Schlaefli symbol
• all chiral polytopes with up to 2000 flags, up to isomorphism, reflection and duality, ordered by the number of flags under each rank
• all chiral polytopes with up to 2000 flags, up to isomorphism, reflection and duality, ordered by their type under each rank

Other information and useful contacts

1. The New Zealand Mathematical Society
2. The New Zealand Journal of Mathematics
3. The Group Pub Forum
4. The World Combinatorics Exchange
5. The Graph Theory White Pages
6. Gordon Royle's Combinatorial catalogues
7. The Mathematics Genealogy Project website.

Address

Prof. M.D.E. Conder
Department of Mathematics
University of Auckland
Private Bag 92019, Auckland
NEW ZEALAND