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Diagonal Orbital


The diagonal orbital of a transitive permutation group Gamma acting on a finite set Omega is the orbital

 {(omega,omega):omega in Omega}.

It consists of the ordered pairs whose two coordinates are equal and is also called the trivial orbital. More generally, if the action of Gamma is not transitive, the diagonal set is the union of one orbital for each orbit of Gamma on Omega. A diagonal orbital is self-paired.


See also

Finite Set, Group Orbit, Orbital, Orbital Digraph, Permutation Group, Self-Paired Orbital

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References

Lauri, J. and Scapellato, R. "Orbital Graphs and Strongly Regular Graphs." Ch. 4 in Topics in Graph Automorphisms and Reconstruction, 2nd ed. Cambridge, England: Cambridge University Press, pp. 64-78, 2016.

Cite this as:

Weisstein, Eric W. "Diagonal Orbital." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/DiagonalOrbital.html

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