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Asymmetric Latin squares, Steiner triple systems, and edge-parallelisms | | Peter J. Cameron
; | | Date: |
8 Jul 2015 | | Abstract: | This article, showing that almost all objects in the title are asymmetric, is
re-typed from a manuscript I wrote somewhere around 1980 (after the papers of
Bang and Friedland on the permanent conjecture but before those of Egorychev
and Falikman). I am not sure of the exact date. The manuscript had been lost,
but surfaced among my papers recently.
I am grateful to Laci Babai and Ian Wanless who have encouraged me to make
this document public, and to Ian for spotting a couple of typos. In the section
on Latin squares, Ian objects to my use of the term "cell"; this might be more
reasonably called a "triple" (since it specifies a row, column and symbol), but
I have decided to keep the terminology I originally used.
The result for Latin squares is in B. D. McKay and I. M. Wanless, On the
number of Latin squares, Annals of Combinatorics 9 (2005), 335-344 (arXiv
0909.2101), while the result for Steiner triple systems is in L. Babai, Almost
all Steiner triple systems are asymmetric, Annals of Discrete Mathematics 7
(1980), 37-39. | | Source: | arXiv, 1507.2190 | | Services: | Forum | Review | PDF | Favorites | |
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