Equivalence classes of Latin squares and nets in

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 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 . Then we count these equivalence classes for small cases. Finally we prove that the realization spaces of these classes in are empty to show some non-existence results for 4-nets in .

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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