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The strongly regular graph with parameters \((100,22,0,6)\): hidden history and beyond. (English) Zbl 1430.05137

Written for the community of algebraic graph theorists, this elaborate and endearingly indulgent tribute to Dale Marsh Mesner (1923–2009) recovers Mesner’s construction in his 1956 thesis and a 1964 set of mimeographed notes of the titular strongly regular graph with parameters \((100,22,0,6)\) and explores a rich collection of associated ideas. Over a decade after Mesner’s initial research, this graph was independently constructed by D. G. Higman and C. C. Sims [Math. Z. 105, 110–113 (1968; Zbl 0186.04002)] alongside a sporadic simple group that marked a milestone in the program to classify all finite simple groups (see [A. Steingart, “A group theory of group theory”, Soc. Stud. Sci. 42, No. 2, 185–213 (2012); doi:10.1177/0306312712436547)]. Examples and illustrations join an extensive biobliography supporting the authors’ effusive and wide-ranging appreciation of Mesner’s work, which the authors regret was not better recognized and appreciated in its time. Those with the requisite familiarity with the relevant branches of combinatorics will find a stimulating perspective on the field inspired by the authors’ association with Mesner. The paper may be read in segments, and begins with a succinct introduction, preliminary conceptual survey, and overview to orient the reader.

MSC:

05E30 Association schemes, strongly regular graphs
05C51 Graph designs and isomorphic decomposition
05B05 Combinatorial aspects of block designs
05B07 Triple systems
05-03 History of combinatorics
01A60 History of mathematics in the 20th century

Citations:

Zbl 0186.04002

Software:

GAP; GRAPE; nauty

References:

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