Some new Kirkman signal sets |
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Authors: | Jezerca Hodaj Melissa S Keranen Donald L Kreher Leah Tollefson |
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Institution: | 1.University College “Pavar?sia Vlor?”,Vlor?,Albania;2.Michigan Technological University,Houghton,USA |
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Abstract: | A decomposition of the blocks of an \(\textsf {STS}(v)\) into partial parallel classes of size m is equivalent to a Kirkman signal set \(\textsf {KSS}(v,m)\). We give decompositions of \(\textsf {STS}(4v-3)\) into classes of size \(v-1\) when \(v \equiv 3 \pmod {6}\), \(v \not = 3\). We also give decompositions of \(\textsf {STS}(v)\) into classes of various sizes when v is a product of two arbitrary integers that are both congruent to \(3 \pmod {6}\). These results produce new families of \(\textsf {KSS}(v,m)\). |
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