Cameron-Liebler k-Classes in PG(2k+1, q)

Abstract

We look at a generalization of Cameron-Liebler line classes to sets of k-spaces, focusing on results in PG(2k+1, q). Here we obtain a connection to k-spreads which parallels the situation for line classes in PG(3,q). After looking at some characterizations of these sets and some of the difficulties that arise in contrast to the known results for line classes, we give some connections to various other geometric objects including k-spreads and Erdős–Ko–Rado sets, and prove results concerning the existence of these objects.

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Correspondence to Morgan Rodgers.

Additional information

The research of M. Rodgers has been supported partially by the FWO project “Moufang verzamelingen” G.0140.09.

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Rodgers, M., Storme, L. & Vansweevelt, A. Cameron-Liebler k-Classes in PG(2k+1, q). Combinatorica 38, 739–757 (2018). https://doi.org/10.1007/s00493-016-3482-y

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Mathematics Subject Classification (2000)

  • 51E20
  • 05B25
  • 05E30