Cycle Systems
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2020
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Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky
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Abstract
In this paper we show that the composition (symmetric difference) ofcycles is well-defined. So, such a collection {. . . , Ci, Ck, . . .} of cycles with a com-position operator,◦, is a matroid. As such, it has sets of independent, or basis,cycles that determine its rankr. This paper is concerned with independent anddependent sets of cycles within a cycle system. In particular, we enumerate thenumber of all possible basis sets in any cycle system of rankr≤6. Then we usea generating function to establish that the ratio of basis sets to all possiblerelementsets approachesc,0.287< c <0.289.
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Mathematics for Applications. 2020 vol. 9, č. 1, s. 55-66. ISSN 1805-3629
http://ma.fme.vutbr.cz/archiv/9_1/ma_9_1_pfaltz_final.pdf
http://ma.fme.vutbr.cz/archiv/9_1/ma_9_1_pfaltz_final.pdf
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en
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© Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky