## Ars Combinatoria, Volume 26Department of Combinatorics and Optimization, University of Waterloo., 1988 - Combinatorial Analysis |

### From inside the book

Results 1-3 of 10

Page 88

It is not possible for one of the 19

Configuration 1, the result is obvious by looking at the disjoint sets 123, 456, 789.

For Configuration 2, consider the sets 123, 456, 478, 9; then any

It is not possible for one of the 19

**quadruples**to have the form NNNN. Proof. ForConfiguration 1, the result is obvious by looking at the disjoint sets 123, 456, 789.

For Configuration 2, consider the sets 123, 456, 478, 9; then any

**quadruple**...Page 89

With no loss of generality, we take the single Qj

must occur with six other numbers and six other letters; suppose that A occurs in

x

With no loss of generality, we take the single Qj

**quadruple**as AN2N2N3. Now Amust occur with six other numbers and six other letters; suppose that A occurs in

x

**quadruples**of the form ALNN and y**quadruples**of the form ALLN. Then we ...Page 64

For partitions H and /,

map to each other in pairs, namely 1234, 1368; 1238, 2578; 5678, 2457; 4567,

1346; eight

3467 ...

For partitions H and /,

**quadruples**1357, 2468 are fixed by /; eight**quadruples**map to each other in pairs, namely 1234, 1368; 1238, 2578; 5678, 2457; 4567,

1346; eight

**quadruples**map in two 4-cycles, namely (1258, 3456, 2378, 1467), (3467 ...

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### Contents

Aldred R E Dept of Mathematics University of Otago P O Box 56 Dunedin | 6 |

Maximal qary Codes and Plotkins Bound | 37 |

Partitioning Sets of Triples into Designs by MJ Sharry and A P Street | 51 |

Copyright | |

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3-colouring adjacent apply Lemma automorphism group balanced ternary Bhaskar Rao designs binomial binomial coefficients bipartite CBTD[p chromatically unique codewords Combinatorial conjugate invariant subgroup construction containing Corollary coset coset graph cubic graph cyclic define denote disjoint edge edge-maximal elements entries equations example exists Fano plane finite field fixes gap sequence triple GBRD give given graph G Hadamard matrices Hamming code Hence hole induced infinite integer flow isomorphic Jennifer Seberry Latin squares Lemma Let G Math Mathematics matroid minimal covers modular cut modulo near-polygonal graph obtain orientation orthogonal PA(n pair partition pentagon system perfect codes periodic gap sequence permutation perpendicular array points weight polynomials prime implicants problem Proof quadruples quaslgroup regulus of rank result Section Segre variety Steiner triple systems subgraph subspace Suppose symmetric Table Theorem Theory valency vectors vertex sequence vertex transitive vertices zero-hole