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By C. J. Colbourn

The scope of the quantity contains all algorithmic and computational features of analysis on combinatorial designs. Algorithmic facets contain new release, isomorphism and research strategies - either heuristic equipment utilized in perform, and the computational complexity of those operations. The scope inside layout conception contains all elements of block designs, Latin squares and their variations, pairwise balanced designs and projective planes and comparable geometries.

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Cohen - - 45 + q" + q'8 + q'6 -1 qJ E7,7 576 cosets 10 double cosets Sizes: 0: 0 111 1: (7) 1 2: (745347) 6: (745634523474563452347) + + + + q25 + g2' + q2' q2' q22 q23 q2' [7] 7: (7456345234745634512347) 8: (74534762345123473456234512347) Some parameters of Lie geometries 31 9: (745347623451 234734562345123473456234512347) I11 q42 Neighbours of a point in 0: 1: I351 Q +J2 + i q 3 + 3q' +Q +Q + 4q5 + 4q6 + 5q7 + 4q8 + 4qo + 3q'O Neigbbours of a point in 1: 0: 11) 1 1: 1121 -1 q q2 ~3 3q4 + 2q6 + q7 2: [18] q5 2g6 4q7 49' 4qo 2q'O + q" 3: [4] q'0 q" + q'2 + q'J Neighbours of a point in 2: 1: IS] l + q +Zq2+q3+q' 2: 1121 -1 q2 q 3 zq4 dq5 + 3q6 + sq7+ q8 3: 1121 q6 2 2 aq8 3qo 2 p + q l l 4: 11) qQ 5: [4] $0 + q" + q ' 2 + q'3 Neighbours of a point in 3: 1: 111 1 + + + + + + + + + + + - -+ + + 2: 191 3: 1121 5: 191 6: 111 + + + + + zq2 + 3q3 + 2q4 + q5 -1 - q2 - q3 + q' + 3q5 + 4q6 + 4q7 + 2q8 + qQ q7 + 2q8 + 3qQ+ 2q'O + q" q 9'' 7: I31 q" + q'2 + q ' 3 Neigbbours of a point in 4: 2: I151 1 + q 2q2 + + + 3q4+ 2q5 + z q 6 -+ q7 + q* -1 - q2 - q 4 + 45 + q' + qQ Q' + q5 + 2q6 + 3q' + 3q8 + 3qQ+ 3q'O + 2q" + q'2 + q'3 4: 10) 5 : IZOl NeighLours of a point in 5: 2: 131 3: pi 4: 111 5: 1121 7: 191 8: 111 +q + + 2q3 + aq4+ 2q5 + -1 - q2 - q3 + 2q5 + 3q6 + sq7 + sq8+ 2qo q8 + 2qQ+ 3q'O + 2q" + q'2 1 q2 q3 q'3 (12 g6 + 2q" 32 A.

M. E. M. (North-Holland) 49 Performance of Subset Generating Algorithms Margaret Carkeet and Peter Eudes Department of Computer Science University of Queensland St. Lucia, Queensland AUSTRALIA Abstract This note reports on some tests of several algorithms for generating the subsets of fixed size of a set. In particular, the speed of execution is compared. 1. Introduction In this note the results of tests of algorithms for generating all subsets of size k of a set of size n (sometimes called combinations) are reported.

The average was taken over n=5 to n=12. The horizontal axis represents the range of k ; the leftmost value is k=2, and the rightmost is C=n-2. The other value of k are dispersed linearly between the left and rightmost. Some statement counts for larger values of n are given in figure 3. 8. Conclusions All the algorithms except EHR are reasonably simple and can be coded in a few pages. LM is very simple and takes only a few minutes to write. No algorithm (exccpt E m ) uses more than O(n) space; this is insignificant in comparison to time requirements.

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