nach oben

Designs, Codes and Cryptography

Erschienen in:

12.09.2018

An Erdős-Ko-Rado theorem for the group \(\hbox {PSU}(3, q)\)

verfasst von: Karen Meagher

Erschienen in: Designs, Codes and Cryptography | Ausgabe 4/2019

Einloggen, um Zugang zu erhalten

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

In this paper we consider the derangement graph for the group \(\mathop {\text {PSU}}(3,q)\), where q is a prime power. We calculate all eigenvalues for this derangement graph and use the eigenvalues to prove that \(\mathop {\text {PSU}}(3,q)\), under its two-transitive action on a set of size \(q^3+1\), has the Erdős-Ko-Rado property and, provided that \(q\ne 2, 5\), another property that we call the Erdős-Ko-Rado module property.

Vorheriger Artikel Preface to the special issue on finite geometries

Nächster Artikel On disjoint difference families

Nur mit Berechtigung zugänglich

Ahmadi B., Meagher K.: A new proof for the Erdős-Ko-Rado theorem for the alternating group. Discret. Math. 324, 28–40 (2014).CrossRefMATH

Ahmadi B., Meagher K.: The Erdős-Ko-Rado property for some \(2\)-transitive groups. Ann. Comb. 19(4), 621–640 (2015).MathSciNetCrossRefMATH

Ahmadi B., Meagher K.: The Erdős-Ko-Rado property for some permutation groups. Aust. J. Comb. 61, 23–41 (2015).MATH

Babai L.: Spectra of Cayley graphs. J. Comb. Theory B. 2, 180–189 (1979).MathSciNetCrossRefMATH

Cameron P.J., Ku C.Y.: Intersecting families of permutations. Eur. J. Comb. 24, 881–890 (2003).MathSciNetCrossRefMATH

Diaconis P., Shahshahani M.: Generating a random permutation with random transpositions. Z. Wahrsch. Verw. Gebiete 57(2), 159–179 (1981).MathSciNetCrossRefMATH

Dixon J.D., Mortimer B.: Permutation Groups. Graduate Texts in Mathematics, vol. 163. Springer, New York (1996).CrossRefMATH

Erdős P., Ko C., Rado R.: Intersection theorems for systems of finite sets. Quart. J. Math. Oxford Ser. 12, 313–320 (1961).MathSciNetCrossRefMATH

Godsil C., Meagher K.: A new proof of the Erdős-Ko-Rado theorem for intersecting families of permutations. Eur. J. Comb. 30, 404–414 (2009).CrossRefMATH

10.

Godsil C., Meagher K.: Erdős-Ko-Rado Theorems: Algebraic Approaches. Cambridge University Press, Cambridge (2015).MATH

11.

Godsil C., Royle G.: Algebraic Graph Theory. Graduate Texts in Mathematics, vol. 207. Springer, New York (2001).CrossRefMATH

12.

Hoffman AJ.: On eigenvalues and colorings of graphs. In: Graph Theory and Its Applications, (Proc. Adv. Sem., Math. Research Center, Univ. of Wisconsin, Madison, WI, 1969). Academic Press, New York (1970).

13.

Ku C.Y., Wong T.W.H.: Intersecting families in the alternating group and direct product of symmetric groups. Electron. J. Comb. 14, 25 (2007). (electronic).MathSciNetMATH

14.

Larose B., Malvenuto C.: Stable sets of maximal size in Kneser-type graphs. Eur. J. Comb. 25, 657–673 (2004).MathSciNetCrossRefMATH

15.

Long L., Plaza R., Sin P.: Qing Xiang characterization of intersecting families of maximum size in \({\mathop {\rm PSL}}(2, q)\). J. Comb. Theory Ser. A 157, 461–499 (2018).CrossRef

16.

Meagher K., Spiga P.: An Erdős-Ko-Rado theorem for the derangement graph of \(\rm PGL(2, q)\) acting on the projective line. J. Comb. Theory Ser. A 118, 532–544 (2011).CrossRefMATH

17.

Meagher K., Spiga P.: An Erdős-Ko-Rado theorem for the derangement graph of \(\rm PGL_3(q)\) acting on the projective plane. SIAM J. Discret. Math. 28, 918–941 (2011).CrossRefMATH

18.

Meagher K., Spiga P.: Pham Huu Tiep, An Erdős-Ko-Rado theorem for finite 2-transitive groups. Eur. J. Comb. 55, 100–118 (2016).CrossRefMATH

19.

Simpson W.A., Frame S.J.: The character tables for \({\rm SL}(3,\, q)\), \({\rm SU}(3,\, q^{2})\), \({\rm PSL}(3,\, q)\), \({\rm PSU}(3,\, q^{2})\). Can. J. Math. 25, 486–494 (1973).CrossRefMATH

20.

The GAP Group, GAP—Groups.: Algorithms, and Programming, Version 4.4.12; (http://www.gap-system.org) (2008).

Titel: An Erdős-Ko-Rado theorem for the group
verfasst von: Karen Meagher
Publikationsdatum: 12.09.2018
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 4/2019
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-018-0537-7

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Weitere Artikel der Ausgabe 4/2019

Linear codes close to the Griesmer bound and the related geometric structures

A variation of the dual hyperoval using presemifields

Fano Kaleidoscopes and their generalizations

Maximal arcs and extended cyclic codes

Relative blocking sets of unions of Baer subplanes

Three homogeneous embeddings of