Cameron-Liebler k-sets in AG(n,q)

Jonathan Mannaert, Jozefien D'haeseleer, Leo Storme, Ferdinand Ihringer

Onderzoeksoutput: Articlepeer review

3 Citaten (Scopus)
12 Downloads (Pure)

Samenvatting

We study Cameron-Liebler k-sets in the affine geometry, so sets of k-spaces in AG(n,q). This generalizes research on Cameron-Liebler k-sets in the projective geometry PG(nq). Note that in algebraic combinatorics, Cameron-Liebler k-sets of AG(nq) correspond to certain equitable bipartitions of the association scheme of k-spaces in AG(n,q), while in the analysis of Boolean functions, they correspond to Boolean degree 1 functions of AG(n,q). We define Cameron-Liebler k-sets in AG(n,q) by intersection properties with k-spreads and show the equivalence of several definitions. In particular, we investigate the relationship between Cameron-Liebler k-sets in AG(n,q) and PG(n,q). As a by-product, we calculate the character table of the association scheme of affine lines. Furthermore, we characterize the smallest examples of Cameron-Liebler k-sets. This paper focuses on AG(n,q) for n >3, while the case for Cameron-Liebler line classes in AG(3,q) was already treated separately.
Originele taal-2English
Artikelnummer11
Pagina's (van-tot)1-31
Aantal pagina's31
TijdschriftElectronic Journal of Combinatorics
Volume28
Nummer van het tijdschrift4
DOI's
StatusPublished - 22 okt 2021

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