Semiboolean SQS-skeins
Andreas J. Guelzow
DOI: 10.1023/A:1022411724747
Abstract
We will present a counter example to the conjecture that the class of boolean SQS-skeins is defined by the equation q( x, u, q( y, u, z)) = q( q( x, u, y), u, z ). The SQS-skeins satisfying this equation will be seen to be exactly those SQS-skeins that correspond to Steiner quadruple systems whose derived Steiner triple systems are all projective geometries.
Pages: 147–153
Keywords: Steiner quadruple system; Steiner triple system; SQS-skein; semiboolean; derived Steiner triple system; projective geometry
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References
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2. M.H. Armanious, "Existence of nilpotent SQS-skeins of class n," An Combin. 29 (1990), 97-105.
3. J. Doyen and M. Vandensavel, "Nonisomorphic Steiner quadruple systems," Bull Soc. Math. Belg. 23 (1971), 393-410.
4. R.S. Freese and R.N. McKenzie, Commutator Theory for Congruence Modular Varieties. Cambridge University Press, Cambridge, MA, 1987.
5. B. Ganter and H. Werner, "Co-ordinatizing Steiner systems," Ann. Discrete Math. 7 (1980), 3-24.
6. A.J. Guelzow, "Some classes of E-minimal algebras of affine type: Nilpotent squags, p-groups and nilpotent SQS-skeins," Ph.D. Thesis, University of Manitoba, 1991.
7. C.C. Lindner and A. Rosa, "Steiner quadruple systems - A survey," Discrete Math. 21 (1978), 147-181.
8. E. Mendelsohn, "On the groups of automorphisms of Steiner triple and quadruple systems," Conference on Algebraic Aspects of Combinatorics, Congressus Numerantium XIII, 1975, 255-264.
9. R.W. Quackenbush, "Algebraic aspects of Steiner quadruple systems," Conference on Algebraic Aspects of Combinatorics, Congressus Numerantium XIII, 1975, 265-268.
10. L. Teirlinck, "Combinatorial properties of planar spaces and embeddability," J. Combin. Theory Ser. A 43 (1986), 291-302.