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Prof. Melissa Keranen: “Some new Kirkman signal sets”

A decomposition of the blocks of an STS(v) into partial parallel classes of size m is equivalent to a Kirkman signal set KSS(v, m). We give decompositions of STS(4v − 3) into classes of size v − 1 when v ≡ 3 (mod 6). We also give decompositions of STS(v) into classes of various sizes when v is a product of two arbitrary integers that are both congruent to 3 (mod 6). These results produce new families of KSS(v, m).