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Automorphisms groups of Walecki tournaments : thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy
Aleš, Janez, 1966-
Lucas tournaments, today known as Walecki tournaments, were defined by Alspach in 1996. A mapping between cycles of the complementing circular shift register and isomorphism classes of Walecki ...tournaments was determined. Alspach conjectured that the bound is tight. The problem of enumerating Walecki tournaments has not been solved to date. However, it was published as an open problem in a paper by Alspach, Bermond, and Sotteau in 1987, and as a research problem by Alspach in 1989. In a attempt to prove this 33 years old conjecture we determine the automorphism groups of Walecki tournaments for all but those whose corresponding binary sequences are aperiodic, or have odd or even pattern with an aperiodic subsequence. Techniques are used in the proof originate from a diverse range of topics: permutation groups, tournaments, and bijective enumeration, to mention a few.
Type of material - dissertation
Publication and manufacture - [Harbour Centre, Vancouver] : [J. Aleš], cop. 2000
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