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Packings of pairs with a minimum known number of quadruples

Jiří Novák (1995)

Mathematica Bohemica

Let E be an n -set. The problem of packing of pairs on E with a minimum number of quadruples on E is settled for n < 15 and also for n = 36 t + i , i = 3 , 6 , 9 , 12 , where t is any positive integer. In the other cases of n methods have been presented for constructing the packings having a minimum known number of quadruples.

Parallel Class Intersection Matrices of Orthogonal Resolutions

Zhelezova, Stela (2008)

Serdica Journal of Computing

This work was partially supported by the Bulgarian National Science Fund under Contract No MM 1405. Part of the results were announced at the Fifth International Workshop on Optimal Codes and Related Topics (OCRT), White Lagoon, June 2007, BulgariaParallel class intersection matrices (PCIMs) have been defined and used in [6], [14], [15] for the classification of resolvable designs with several parameter sets. Resolutions which have orthogonal resolutions (RORs) have been classified in [19] for designs...

Parallelepipeds, nilpotent groups and Gowers norms

Bernard Host, Bryna Kra (2008)

Bulletin de la Société Mathématique de France

In his proof of Szemerédi’s Theorem, Gowers introduced certain norms that are defined on a parallelepiped structure. A natural question is on which sets a parallelepiped structure (and thus a Gowers norm) can be defined. We focus on dimensions 2 and 3 and show when this possible, and describe a correspondence between the parallelepiped structures and nilpotent groups.

Partial Ovoids and Partial Spreads of Classical Finite Polar Spaces

De Beule, J., Metsch, K., Klein, A., Storme, L. (2008)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 05B25, 51E20.We survey the main results on ovoids and spreads, large maximal partial ovoids and large maximal partial spreads, and on small maximal partial ovoids and small maximal partial spreads in classical finite polar spaces. We also discuss the main results on the spectrum problem on maximal partial ovoids and maximal partial spreads in classical finite polar spaces.The research of the fourth author was also supported by the Project Combined algorithmic...

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