On thep-Rank of the Incidence Matrix of a Projective Hjelmslev Plane

Maryam Bajalan; Ivan Landjev; Assia Rousseva

Computer Science and Education in Computer Science. 19th EAI International Conference, CSECS 2023, Boston, MA, USA, June 28–29, 2023, Proceedings

Research Article

On thep-Rank of the Incidence Matrix of a Projective Hjelmslev Plane

Cite: BibTeX Plain Text

@INPROCEEDINGS{10.1007/978-3-031-44668-9_2,
    author={Maryam Bajalan and Ivan Landjev and Assia Rousseva},
    title={On thep-Rank of the Incidence Matrix of a Projective Hjelmslev Plane},
    proceedings={Computer Science and Education in Computer Science. 19th EAI International Conference, CSECS 2023, Boston, MA, USA, June 28--29, 2023, Proceedings},
    proceedings_a={CSECS},
    year={2023},
    month={10},
    keywords={projective Hjelmslev plane finite chain ring incidence matrix p-rank},
    doi={10.1007/978-3-031-44668-9_2}
}

Maryam Bajalan
Ivan Landjev
Assia Rousseva
Year: 2023
On thep-Rank of the Incidence Matrix of a Projective Hjelmslev Plane
CSECS
Springer
DOI: 10.1007/978-3-031-44668-9_2

Maryam Bajalan¹, Ivan Landjev¹^,*, Assia Rousseva²

1: Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 8 Acad. G. Bonchev str.
2: Faculty of Mathematics and Informatics, Sofia University, 5 J. Bourchier blvd.

*Contact email: ivan@math.bas.bg

Abstract

In this paper we estimate thep-rank of the points-by-lines incidence matrix of a projective Hjelmslev plane over a chain ring with 4 or 9 elements. The proof uses a characterization of all divisible arcs in the corresponding projective planes. Furthermore, we prove lower and upper bounds on thep-rank of the incidence matrix of the projective Hjelmslev plane over an arbitrary finite chain ring of nilpotency index 2.

Keywords: projective Hjelmslev plane finite chain ring incidence matrix p-rank

Published: 2023-10-11
Appears in: SpringerLink

: http://dx.doi.org/10.1007/978-3-031-44668-9_2

On thep-Rank of the Incidence Matrix of a Projective Hjelmslev Plane

Abstract

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