Lübeck, Frank; Neunhöffer, Max Enumerating large orbits and direct condensation. (English) Zbl 1044.20006 Exp. Math. 10, No. 2, 197-205 (2001). Summary: We describe a new algorithm for ‘direct condensation’, which is a tool in computational representation theory. The crucial point for this is the enumeration of very large orbits for a group acting on some set. We present a variation of the standard orbit enumeration algorithm that reduces the amount of storage needed and behaves well under parallelization. For the special case of matrices acting on a finite vector space an efficient implementation is described. This allows us to use condensation methods for considerably larger permutation representations than could be handled before. Cited in 1 ReviewCited in 9 Documents MSC: 20C40 Computational methods (representations of groups) (MSC2010) 20C20 Modular representations and characters 20C30 Representations of finite symmetric groups 68W30 Symbolic computation and algebraic computation Keywords:computational representation theory; orbit enumeration algorithms; modular representations; orbits; finite permutation groups; linear groups; condensation methods; symmetric groups Software:GAP; MeatAxe; MPI × Cite Format Result Cite Review PDF Full Text: DOI Euclid EuDML References: [1] Cooperman, G. and Tselman, M. ”New sequential and parallel algorithms for generating high dimension Hecke algebras using the condensation technique”. ISSAC1996: Proceedings of the International Symposium on Symbolic and Algebraic Computation. 1996, Zurich. Edited by: Lakshman, Y. N. pp.155–160. New York: ACM Press. [Cooperman and Tselman 1996] · Zbl 0916.20007 [2] DOI: 10.1080/10586458.1997.10504617 · Zbl 1115.20307 · doi:10.1080/10586458.1997.10504617 [3] GAP: Groups, algorithms, and programming, Version 4.2 (2000) [4] Knuth D. E., The art of computer programming, v. 3: Sorting and searching,, 2. ed. (1997) · Zbl 0883.68015 [5] Mathas A., Specht: Decomposition matrices for the Hecke algebras of type A (manual for version 2.4) (1997) [6] Ringe M., The C-MeatAxe, a manual (1998) [7] Snir M., MPI–the complete reference,, 2. ed. (1998) [8] Thackray J. G., Ph.D. thesis, in: Modular representations of finite groups (1981) [9] Wilson R., ”WWW-Atlas of group representations” (1996) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.