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Incomplete idempotent Schröder quasigroups and related packing designs (1996)

Bennett, F. E. ; Wei, R. ; Zhu, L.

Springer

Aequationes mathematicae 51 (1996), S. 100-114

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ISSN: 1420-8903

Keywords: Primary 05B05, 05B15, 20N05 ; Secondary 05B40

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Summary In this paper it is proved that, for any positive integern ≡ 2, 3 (mod 4),n ≥ 7, there exists an incomplete idempotent Schröder quasigroup with one hole of size two IISQ(n, 2) except forn = 10. It is also proved that for any positive integern ≡ 0, 1 (mod 4), there exists an idempotent Schröder quasigroup ISQ(n) except forn = 5 and 9. These results completely determine the spectrum of ISQ(n) and provide an application to the packing of a class of edge-coloured block designs.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01831143

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