Prof Mike Grannell
Emeritus Professor
School of Mathematics & Statistics
Biography
Professional biography
I am an Emeritus Professor in the School of Mathematics and Statistics within the Faculty of Science, Technology, Engineering and Mathematics at the Open University.
The postal address is: School of Mathematics and Statistics, The Open University, Walton Hall, Milton Keynes, MK7 6AA, U.K.
You can email me at: mike.grannell@open.ac.uk
My research area is combinatorics, in particular block designs and Steiner systems.
For more information on research publications, and some educational materials, see my own home page (https://grannell.net/mike.html).
Publications
Book Chapter
Journal Article
On maximal partial Latin hypercubes (2024)
Avoidance in bowtie systems (2022)
Anti-Pasch optimal coverings with triples (2021)
Embedding partial Latin squares in Latin squares with many mutually orthogonal mates (2020)
Maximum partial triple systems on 16 and 17 points (2020)
Anti-Pasch optimal packings with triples (2019)
On the number of transversals in a class of Latin squares (2018)
On the number of additive permutations and Skolem-type sequences (2018)
Pasch trades on the projective triple system of order 31 (2016)
Identical twin Steiner triple systems (2016)
Biembeddings of 2-rotational Steiner triple systems (2015)
Rigid Steiner triple systems obtained from projective triple systems (2014)
Doubly even orientable closed 2-cell embeddings of the complete graph. (2014)
Coloring cubic graphs by point-intransitive Steiner triple systems (2013)
Maximizing the number of Pasch configurations in a Steiner triple system (2013)
On the number of transversal designs (2013)
Configurations in bowtie systems (2013)
Dihedral biembeddings and triangulations by complete and complete tripartite graphs (2013)
Even-cycle systems with prescribed automorphism groups (2013)
On the number of triangular embeddings of complete graphs and complete tripartite graphs (2012)
On the number of designs with affine parameters (2012)
Biembedding Abelian groups with mates having transversals (2012)
A construction for biembeddings of Latin squares (2011)
Biembeddings of Latin squares obtained from a voltage construction (2011)
Pasch trades with a negative block (2011)
Designs having the parameters of projective and affine spaces (2011)
Self-embeddings of cyclic and projective Steiner quasigroups (2011)
On parity vectors of Latin squares (2010)
Third-regular bi-embeddings of Latin squares (2010)
Some rigid Steiner 5-designs (2010)
An enumeration of minimum genus orientable embeddings of some complete bipartite graphs (2010)
Properties of the Steiner Triple Systems of Order 19 (2010)
A lower bound for the number of orientable triangular embeddings of some complete graphs (2010)
On sparse countably infinite Steiner triple systems (2010)
Biembeddings of Abelian groups (2010)
Quarter-regular biembeddings of Latin squares (2010)
A constraint on the biembedding of Latin squares (2009)
Orientable biembeddings of Steiner triple systems of order 15 (2009)
Smallest defining sets of directed triple systems (2009)
Wilson-Schreiber colourings of cubic graphs (2009)
Small bowtie systems: an enumeration (2009)
Bounds on g(1)((5)) (v) for v equivalent to 9, 13, 17 (mod 20) (2009)
Further 6-sparse Steiner Triple Systems (2009)
On biembeddings of Latin squares (2009)
Biembeddings of symmetric configurations and 3-homogeneous Latin trades (2008)
A census of the orientable biembeddings of Steiner triple systems of order 15 (2008)
New type B colorable S(2, 4, v) designs (2007)
On 6-sparse Steiner triple systems (2007)
Biembeddings of Latin squares of side 8 (2007)
The design of the century (2007)
On the small covering numbers $g^{(5)}_1(v)$ (2007)
Distance and fractional isomorphism in Steiner triple systems (2007)
Hamiltonian embeddings from triangulations (2007)
Small surface trades in triangular embeddings (2006)
A flaw in the use of minimal defining sets for secret sharing schemes (2006)
Triangulations of orientable surfaces by complete tripartite graphs (2006)
Diagonally switchable 4-cycle systems (2006)
Orientable self-embeddings of Steiner triple systems of order 15 (2006)
Maximum genus embeddings of Steiner triple systems (2005)
On the covering number $g_1^{(4)}(18)$ (2005)
Large sets of cycle systems on nine points (2005)
Steiner triple systems and existentially closed graphs (2005)
Biembeddings of Latin squares and Hamiltonian decompositions (2004)
Exponential lower bounds for the numbers of Skolem-type sequences (2004)
Nonorientable biembeddings of Steiner triple systems (2004)
Independent sets in Steiner triple systems (2004)
Configurations in 4-cycle systems (2004)
A Steiner triple system which colours all cubic graphs (2004)
Configurations and trades in Steiner triple systems (2004)
On $\lambda$-fold coverings with maximum block size four for $\lambda\ge 6$ (2004)
On $\lambda$-fold coverings with maximum block size four for $\lambda = 3, 4$ and 5 (2004)
Non-orientable biembeddings of Steiner triple systems of order 15 (2004)
Minimal perfect bicoverings of Kv with block sizes two, three and four (2004)
On the minimal nonzero distance between triangular embeddings of a complete graph (2003)
Face two-colourable triangulations of $K_{13}$ (2003)
More on exact bicoverings of 12 points (2003)
Large sets of large sets of Steiner triple systems of order 9 (2003)
On the volume of 4-cycle trades (2003)
On colourings of Steiner triple systems (2003)
On the bi-embeddability of certain Steiner triple systems of order 15 (2002)
On large sets of v-1 L-intersecting Steiner triple systems of order v (2002)
Cyclic bi-embeddings of Steiner triple systems on 12s+7 points (2002)
Recursive constructions for triangulations (2002)
Modular gracious labellings of trees (2001)
Bi-embeddings of Steiner triple systems of order 15 (2001)
Cyclic bi-embeddings of Steiner triple systems on 31 points (2001)
The Triangle chromatic index of Steiner triple systems (2001)
On exact bicoverings of 12 points (2000)
On directed designs with block size five (2000)
Bi-embeddings of the projective space PG(3,2) (2000)
Exponential families of non-isomorphic triangulations of complete graphs (2000)
Three-line chromatic indices of Steiner triple systems (2000)
Pairwise balanced designs on $4s+1$ points with longest block of cardinality $2s$ (2000)
All admissible $3$-$(v, 4, \lambda)$ directed designs exist (2000)
Non-isomorphic solutions for some triple systems with bipoints (2000)
Proper edge-colourings of complete graphs (2000)
Triple systems with tripoints (2000)
The resolution of the anti-Pasch conjecture (2000)
Construction techniques for anti-Pasch Steiner triple systems (2000)
