Equivalence classes of Latin squares and nets in ℂ P 2

Corey Dunn; Matthew Miller; Max Wakefield; Sebastian Zwicknagl

Annales de la faculté des sciences de Toulouse Mathématiques (2014)

  • Volume: 23, Issue: 2, page 335-351
  • ISSN: 0240-2963

Abstract

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The fundamental combinatorial structure of a net in ℂ P 2 is its associated set of mutually orthogonal Latin squares. We define equivalence classes of sets of orthogonal Latin squares by label equivalences of the lines of the corresponding net in ℂ P 2 . Then we count these equivalence classes for small cases. Finally we prove that the realization spaces of these classes in ℂ P 2 are empty to show some non-existence results for 4-nets in ℂ P 2 .

How to cite

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Dunn, Corey, et al. "Equivalence classes of Latin squares and nets in ${\mathbb{C}P}^2$." Annales de la faculté des sciences de Toulouse Mathématiques 23.2 (2014): 335-351. <http://eudml.org/doc/275313>.

@article{Dunn2014,
abstract = {The fundamental combinatorial structure of a net in $\scriptstyle \mathbb\{C\}P^2$ is its associated set of mutually orthogonal Latin squares. We define equivalence classes of sets of orthogonal Latin squares by label equivalences of the lines of the corresponding net in $\scriptstyle \mathbb\{C\}P^2$. Then we count these equivalence classes for small cases. Finally we prove that the realization spaces of these classes in $\scriptstyle \mathbb\{C\}P^2$ are empty to show some non-existence results for 4-nets in $\scriptstyle \mathbb\{C\}P^2$.},
author = {Dunn, Corey, Miller, Matthew, Wakefield, Max, Zwicknagl, Sebastian},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {nets; Latin squares},
language = {eng},
month = {3},
number = {2},
pages = {335-351},
publisher = {Université Paul Sabatier, Toulouse},
title = {Equivalence classes of Latin squares and nets in $\{\mathbb\{C\}P\}^2$},
url = {http://eudml.org/doc/275313},
volume = {23},
year = {2014},
}

TY - JOUR
AU - Dunn, Corey
AU - Miller, Matthew
AU - Wakefield, Max
AU - Zwicknagl, Sebastian
TI - Equivalence classes of Latin squares and nets in ${\mathbb{C}P}^2$
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2014/3//
PB - Université Paul Sabatier, Toulouse
VL - 23
IS - 2
SP - 335
EP - 351
AB - The fundamental combinatorial structure of a net in $\scriptstyle \mathbb{C}P^2$ is its associated set of mutually orthogonal Latin squares. We define equivalence classes of sets of orthogonal Latin squares by label equivalences of the lines of the corresponding net in $\scriptstyle \mathbb{C}P^2$. Then we count these equivalence classes for small cases. Finally we prove that the realization spaces of these classes in $\scriptstyle \mathbb{C}P^2$ are empty to show some non-existence results for 4-nets in $\scriptstyle \mathbb{C}P^2$.
LA - eng
KW - nets; Latin squares
UR - http://eudml.org/doc/275313
ER -

References

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