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  • 1
    Electronic Resource
    Electronic Resource
    Incomplete idempotent Schröder quasigroups and related packing designs (1996)
    Springer
    Aequationes mathematicae 51 (1996), S. 100-114 
    Details
    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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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Perfect Mendelsohn Packing Designs with Block Size Five (1998)
    Springer
    Designs, codes and cryptography 14 (1998), S. 5-22 
    Details
    ISSN: 1573-7586
    Keywords: perfect Mendelsohn packing designs ; incomplete perfect Mendelsohn designs ; transversal designs
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A (v, k, 1) perfect Mendelsohn packing design (briefly (v, k, 1)-PMPD) is a pair (X, A) where X is a v-set (of points) and A is a collection of cyclically ordered k-subsets of X (called blocks) such that every ordered pair of points of X appears t-apart in at most one block of A for all t = 1, 2,..., k-1. If no other such packing has more blocks, the packing is said to be maximum and the number of blocks in a maximum packing is called the packing number, denoted by P(v, k, 1). The values of the function P(v, 5, 1) are determined here for all v ≥5 with a few possible exceptions. This result is established by means of a result on incomplete perfect Mendelsohn designs which is of interest in its own right.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008200319697
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    Paper (German National Licenses)
    Fulltext
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