There is no McLaughlin geometry

Patric R.J. Östergård; Leonard H. Soicher

doi:10.1016/j.jcta.2017.10.004

There is no McLaughlin geometry

Patric R.J. Östergård, Leonard H. Soicher

Tutkimustuotos: Lehtiartikkeli › Article › Scientific › vertaisarvioitu

Abstrakti

We determine that there is no partial geometry G with parameters (s,t,α)=(4,27,2). The existence of such a geometry has been a challenging open problem of interest to researchers for almost 40 years. The particular interest in G is due to the fact that it would have the exceptional McLaughlin graph as its point graph. Our proof makes extensive use of symmetry and high-performance distributed computing, and details of our techniques and checks are provided. One outcome of our work is to show that a pseudogeometric strongly regular graph achieving equality in the Krein bound need not be the point graph of any partial geometry.

Alkuperäiskieli	Englanti
Sivut	27-41
Sivumäärä	15
Julkaisu	Journal of Combinatorial Theory. Series A
Vuosikerta	155
DOI - pysyväislinkit	https://doi.org/10.1016/j.jcta.2017.10.004
Tila	Julkaistu - 1 huhtikuuta 2018
OKM-julkaisutyyppi	A1 Julkaistu artikkeli, soviteltu

Pääsy asiakirjaan

10.1016/j.jcta.2017.10.004

Link to publication in Scopus

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Siteeraa tätä

Östergård, P. R. J., & Soicher, L. H. (2018). There is no McLaughlin geometry. Journal of Combinatorial Theory. Series A, 155, 27-41. https://doi.org/10.1016/j.jcta.2017.10.004

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AU - Soicher, Leonard H.

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KW - Krein bound

KW - McLaughlin geometry

KW - McLaughlin graph

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