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Discrete Laplace cycles of period four

Hans-Peter Schröcker (2012)

Open Mathematics

We study discrete conjugate nets whose Laplace sequence is of period four. Corresponding points of opposite nets in this cyclic sequence have equal osculating planes in different net directions, that is, they correspond in an asymptotic transformation. We show that this implies that the connecting lines of corresponding points form a discrete W-congruence. We derive some properties of discrete Laplace cycles of period four and describe two explicit methods for their construction.

Disjoint and complete unions of incidence structures

František Machala, Marek Pomp (1997)

Mathematica Bohemica

Some decompositions of general incidence structures with regard to distinguished components (modular or simple) are considered and several structure theorems for them are deduced.

Divisible designs admitting a Suzuki group as an automorphism group

Ralph-Hardo Schulz, Antonino~Giorgio Spera (1998)

Bollettino dell'Unione Matematica Italiana

Si costruiscono, facendo uso delle rette dei piani di Lüneburg e degli ovali di Tits, due classi di disegni divisibili ipersemplici che ammettono il gruppo di Suzuki S q ( q = 2 2 t + 1 con t 1 ) come gruppo di automorfismi. Inoltre si studiano le strutture ottenute determinandone le orbite di S q .

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