Gordon Royle
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View article: Tactical decompositions in finite polar spaces and non-spreading classical group actions
Tactical decompositions in finite polar spaces and non-spreading classical group actions Open
For finite classical groups acting naturally on the set of points of their ambient polar spaces, the symmetry properties of synchronising and separating are equivalent to natural and well-studied problems on the existence of certain config…
View article: Cubic graphs with no eigenvalues in the interval (-1,1)
Cubic graphs with no eigenvalues in the interval (-1,1) Open
We give a complete characterisation of the cubic graphs with no eigenvalues in the open interval $(-1,1)$. There are two infinite families, one due to Guo and Mohar [Linear Algebra Appl. 449:68--75] the other due to Kollár and Sarnak [Comm…
View article: Triangle-free graphs with diameter 2
Triangle-free graphs with diameter 2 Open
There are finitely many graphs with diameter $2$ and girth 5. What if the girth 5 assumption is relaxed? Apart from stars, are there finitely many triangle-free graphs with diameter $2$ and no $K_{2,3}$ subgraph? This question is related t…
View article: Tactical decompositions in finite polar spaces and non-spreading classical group actions
Tactical decompositions in finite polar spaces and non-spreading classical group actions Open
For finite classical groups acting naturally on the set of points of their ambient polar spaces, the symmetry properties of \emph{synchronising} and \emph{separating} are equivalent to natural and well-studied problems on the existence of …
View article: P675: IMATINIB THERAPY IN PREVIOUSLY UNTREATED CHRONIC MYELOID LEUKAEMIA PATIENTS WHO ACHIEVE MMR AFTER 12 MONTHS THERAPY WITH DASATINIB: A STRATEGY TO AVOID LONG TERM OFF TARGET TOXICITY
P675: IMATINIB THERAPY IN PREVIOUSLY UNTREATED CHRONIC MYELOID LEUKAEMIA PATIENTS WHO ACHIEVE MMR AFTER 12 MONTHS THERAPY WITH DASATINIB: A STRATEGY TO AVOID LONG TERM OFF TARGET TOXICITY Open
Background: Despite the impressive outcomes seen with tyrosine kinase inhibitor (TKI) therapy in chronic myeloid leukaemia (CML), the optimal upfront therapy remains unclear. Second generation TKI (2G TKI) trials have shown significantly m…
View article: Direct oral anticoagulants or vitamin K antagonists in emergencies: comparison of management in an observational study
Direct oral anticoagulants or vitamin K antagonists in emergencies: comparison of management in an observational study Open
In DOAC patients, when compared to those receiving VKA, plasma DOAC levels were measured less frequently than the international normalized ratio and had a poor relationship with administering a hemostatic reversal agent. In addition, follo…
View article: Tournaments and even graphs are equinumerous
Tournaments and even graphs are equinumerous Open
A graph is called odd if there is an orientation of its edges and an automorphism that reverses the sense of an odd number of its edges and even otherwise. Pontus von Brömssen (né Andersson) showed that the existence of such an automorphis…
View article: Separating rank 3 graphs
Separating rank 3 graphs Open
We classify, up to some notoriously hard cases, the rank 3 graphs which fail to meet either the Delsarte or the Hoffman bound. As a consequence, we resolve the question of separation for the corresponding rank 3 primitive groups and give n…
View article: Matroids with 9 elements
Matroids with 9 elements Open
This dataset contains the 385370 pairwise non-isomorphic matroids from 0 to 9 elements inclusive. Each matroid is given as a text string occupying one line of the file matroids09_rankLine. Except for the empty matroid, the text string give…
View article: Matroids with 9 elements
Matroids with 9 elements Open
This dataset contains the 385370 pairwise non-isomorphic matroids from 0 to 9 elements inclusive. Each matroid is given as a text string occupying one line of the file matroids09_rankLine. Except for the empty matroid, the text string give…
View article: Synchronising primitive groups of diagonal type exist
Synchronising primitive groups of diagonal type exist Open
Every synchronising permutation group is primitive and of one of three types:\naffine, almost simple, or diagonal. We exhibit the first known example of a\nsynchronising diagonal type group. More precisely, we show that\n$\\mathrm{PSL}(2,q…
View article: Tournaments and Even Graphs are Equinumerous
Tournaments and Even Graphs are Equinumerous Open
A graph is called odd if there is an orientation of its edges and an automorphism that reverses the sense of an odd number of its edges, and even otherwise. Pontus von Brömssen (né Andersson) showed that the existence of such an automorphi…
View article: Transitive groups of degree 48
Transitive groups of degree 48 Open
This database contains the transitive groups of degree 48. It is intended to be used in GAP, but also to be accessible more generally. The groups were originally computed by Derek Holt using MAGMA; this computation was reported in the foll…
View article: Transitive groups of degree 48
Transitive groups of degree 48 Open
This database contains the transitive groups of degree 48. It is intended to be used in GAP, but also to be accessible more generally. The groups were originally computed by Derek Holt using MAGMA; this computation was reported in the foll…
View article: Synchronising primitive groups of diagonal type exist
Synchronising primitive groups of diagonal type exist Open
Every synchronising permutation group is primitive and of one of three types: affine, almost simple, or diagonal. We exhibit the first known example of a synchronising diagonal type group. More precisely, we show that $\mathrm{PSL}(2,q)\ti…
View article: Chromatic roots at 2 and the Beraha number B<sub>10</sub>
Chromatic roots at 2 and the Beraha number B<sub>10</sub> Open
By the construction of suitable graphs and the determination of their chromatic polynomials, we resolve two open questions concerning real chromatic roots. First we exhibit graphs for which the Beraha number (Formula presented.) is a chrom…
View article: Vertex-transitive Graphs On Fewer Than 48 Vertices
Vertex-transitive Graphs On Fewer Than 48 Vertices Open
Vertex-transitive Graphs On Fewer Than 48 Vertices This dataset contains all the vertex-transitive graphs on 10-47 vertices. It consists of a collection of tar files, with names like alltrans26.tar meaning that this tar file contains all t…
View article: Vertex-transitive Graphs On Fewer Than 48 Vertices
Vertex-transitive Graphs On Fewer Than 48 Vertices Open
Vertex-transitive Graphs On Fewer Than 48 Vertices This dataset contains all the vertex-transitive graphs on 10-47 vertices. It consists of a collection of tar files, with names like alltrans26.tar meaning that this tar file contains all t…
View article: Evidence of impaired dabigatran absorption following laparoscopic Roux‐en‐Y gastric bypass surgery: the Auckland regional experience (2011–2018)
Evidence of impaired dabigatran absorption following laparoscopic Roux‐en‐Y gastric bypass surgery: the Auckland regional experience (2011–2018) Open
Obesity represents a significant public health problem across the developed world. Bariatric surgery is considered the most effective treatment option for morbidly obese individuals in whom non-surgical weight loss has proved unsuccessful,…
View article: On the flip graphs on perfect matchings of complete graphs and signed reversal graphs
On the flip graphs on perfect matchings of complete graphs and signed reversal graphs Open
In this paper, we study the flip graph on the perfect matchings of a complete graph of even order. We investigate its combinatorial and spectral properties including connections to the signed reversal graph and we improve a previous upper …
View article: Chromatic roots at 2 and the Beraha number B10
Chromatic roots at 2 and the Beraha number B10 Open
By the construction of suitable graphs and the determination of their chromatic polynomials, we resolve two open questions concerning real chromatic roots. First we exhibit graphs for which the Beraha number is a chromatic root. As it was …
View article: Groups generated by derangements
Groups generated by derangements Open
We examine the subgroup $D(G)$ of a transitive permutation group $G$ which is generated by the derangements in $G$. Our main results bound the index of this subgroup: we conjecture that, if $G$ has degree $n$ and is not a Frobenius group, …
View article: Designs in Endlicher Geometrie
Designs in Endlicher Geometrie Open
This thesis is concerned with the study of Delsarte designs in symmetric association schemes, particularly in the context of finite geometry. We prove that m-ovoids of regular near polygons satisfying certain conditions must be hemisystems…
View article: Transversal polynomial of r-fold covers
Transversal polynomial of r-fold covers Open
We explore the interplay between algebraic combinatorics and algorithmic problems in graph theory by defining a polynomial with connections to correspondence colouring (also known as DP-colouring), a recent generalization of list-colouring…
View article: Structure of Cubic Lehman Matrices
Structure of Cubic Lehman Matrices Open
A pair $(A,B)$ of square $(0,1)$-matrices is called a Lehman pair if $AB^T=J+kI$ for some integer $k\in\{-1,1,2,3,\ldots\}$. In this case $A$ and $B$ are called Lehman matrices. This terminology arises because Lehman showed that the rows w…