Page 276 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 276
CONFIGURATIONS (MS-81)
Strongly regular configurations
Vedran Krcˇadinac, vedran.krcadinac@math.hr
University of Zagreb Faculty of Science, Croatia
Coauthors: Marien Abreu, Martin Funk, Domenico Labbate
We report on the recent study [1] of combinatorial configurations with the associated point and
line graphs being strongly regular. A prominent family of such configurations are the partial
geometries, introduced by R. C. Bose in 1963. We focus on such configurations that are not
partial geometries nor known generalisations such as semipartial geometries and strongly reg-
ular (α, β)-geometries, neither are they elliptic semiplanes of P. Dembowski. Several families
are constructed, necessary existence conditions are proved, and a table of feasible parameters
with at most 200 points is presented.
References
[1] M. Abreu, M. Funk, V. Krcˇadinac, D. Labbate, Strongly regular configurations, preprint,
2021. https://arxiv.org/abs/2104.04880
Hirzebruch-type inequalities and extreme point-line configurations
Piotr Pokora, piotr.pokora@up.krakow.pl
Pedagogical University of Cracow, Poland
In my talk I would like to report on very recent developments devoted to extreme point-line
configurations from an algebraic perspective of Hirzebruch-type inequalities. We recall some
inequalities, especially the most powerful variant based on orbifolds, and then I will report on
extreme combinatorial problems for which Hirzebruch-type inequalities played a decisive role.
Time permitting, we will present a short proof of the Weak Dirac Conjecture.
4-lateral matroids induced by n3-configurations
Michael Raney, mwr23@georgetown.edu
Georgetown University, United States
A 4-lateral matroid induced by an n3-configuration is a rank-4 matroid whose ground set con-
sists of the blocks (lines) of the configuration, and for which any 4 elements of the ground set
are independent if and only if they do not determine a 4-lateral within the configuration. We
characterize the n3-configurations which induce 4-lateral matroids, and provide examples of
small n3-configurations which do so.
274
Strongly regular configurations
Vedran Krcˇadinac, vedran.krcadinac@math.hr
University of Zagreb Faculty of Science, Croatia
Coauthors: Marien Abreu, Martin Funk, Domenico Labbate
We report on the recent study [1] of combinatorial configurations with the associated point and
line graphs being strongly regular. A prominent family of such configurations are the partial
geometries, introduced by R. C. Bose in 1963. We focus on such configurations that are not
partial geometries nor known generalisations such as semipartial geometries and strongly reg-
ular (α, β)-geometries, neither are they elliptic semiplanes of P. Dembowski. Several families
are constructed, necessary existence conditions are proved, and a table of feasible parameters
with at most 200 points is presented.
References
[1] M. Abreu, M. Funk, V. Krcˇadinac, D. Labbate, Strongly regular configurations, preprint,
2021. https://arxiv.org/abs/2104.04880
Hirzebruch-type inequalities and extreme point-line configurations
Piotr Pokora, piotr.pokora@up.krakow.pl
Pedagogical University of Cracow, Poland
In my talk I would like to report on very recent developments devoted to extreme point-line
configurations from an algebraic perspective of Hirzebruch-type inequalities. We recall some
inequalities, especially the most powerful variant based on orbifolds, and then I will report on
extreme combinatorial problems for which Hirzebruch-type inequalities played a decisive role.
Time permitting, we will present a short proof of the Weak Dirac Conjecture.
4-lateral matroids induced by n3-configurations
Michael Raney, mwr23@georgetown.edu
Georgetown University, United States
A 4-lateral matroid induced by an n3-configuration is a rank-4 matroid whose ground set con-
sists of the blocks (lines) of the configuration, and for which any 4 elements of the ground set
are independent if and only if they do not determine a 4-lateral within the configuration. We
characterize the n3-configurations which induce 4-lateral matroids, and provide examples of
small n3-configurations which do so.
274
