Page 278 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 278
CONFIGURATIONS (MS-81)
originate from the two-qubit doily by selecting in the latter a geometric hyperplane and formally
adding to each two-qubit observable, at the same position, the identity matrix if an observable
lies on the hyperplane and the same Pauli matrix for any other observable. Further, given a
doily and any of its geometric hyperplanes, there are other three doilies possessing the same
hyperplane. There is also a particular type of doilies a representative of which features a point
each line through which is negative.
Barycentric configurations in real space
Hendrik Van Maldeghem, Hendrik.VanMaldeghem@UGent.be
Ghent University, Belgium
Barycentric configurations are configurations with three points per line in real projective space
such that (homogeneous) coordinates exist with the property that, for each line, the sum of
the coordinate tuples of the three points on that line is the zero tuple. Such configurations
turn up naturally and we develop some theory about them. In particular there exist universal
barycentric embeddings and a general construction method if the geometry is self-polar. We
apply these results to the Biggs-Smith geometry on 102 points, providing a (new) geometric
construction of the Biggs-Smith graph making the full automorphism group apparent. We also
mention a connection with ovoids.
276
originate from the two-qubit doily by selecting in the latter a geometric hyperplane and formally
adding to each two-qubit observable, at the same position, the identity matrix if an observable
lies on the hyperplane and the same Pauli matrix for any other observable. Further, given a
doily and any of its geometric hyperplanes, there are other three doilies possessing the same
hyperplane. There is also a particular type of doilies a representative of which features a point
each line through which is negative.
Barycentric configurations in real space
Hendrik Van Maldeghem, Hendrik.VanMaldeghem@UGent.be
Ghent University, Belgium
Barycentric configurations are configurations with three points per line in real projective space
such that (homogeneous) coordinates exist with the property that, for each line, the sum of
the coordinate tuples of the three points on that line is the zero tuple. Such configurations
turn up naturally and we develop some theory about them. In particular there exist universal
barycentric embeddings and a general construction method if the geometry is self-polar. We
apply these results to the Biggs-Smith geometry on 102 points, providing a (new) geometric
construction of the Biggs-Smith graph making the full automorphism group apparent. We also
mention a connection with ovoids.
276
