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 .
La structure combinatoire fondamentale d’un filet dans est donnée par l’ensemble des carrés latins orthogonaux associé. Nous définissons des classes d’équivalence de carrés latins orthogonaux a l’aide de classes d’équivalence des lignes apparaisant dans le filet de . Nous comptons le nombre de classes d’équivalence pour certains exemples de carrés petits. Finalement, nous montrons que les espaces de réalisations de ces classes pour et sont vides et nous en déduisons que les filets correspondants n’existent pas.
@article{AFST_2014_6_23_2_335_0,
author = {Corey Dunn and Matthew Miller and Max Wakefield and Sebastian Zwicknagl},
title = {Equivalence classes of {Latin} squares and nets in ${\mathbb{C}P}^2$},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {335--351},
publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques},
address = {Toulouse},
volume = {Ser. 6, 23},
number = {2},
year = {2014},
doi = {10.5802/afst.1409},
mrnumber = {3205596},
zbl = {1296.05030},
language = {en},
url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1409/}
}
TY - JOUR
AU - Corey Dunn
AU - Matthew Miller
AU - Max Wakefield
AU - Sebastian Zwicknagl
TI - Equivalence classes of Latin squares and nets in ${\mathbb{C}P}^2$
JO - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY - 2014
SP - 335
EP - 351
VL - 23
IS - 2
PB - Université Paul Sabatier, Institut de Mathématiques
PP - Toulouse
UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1409/
DO - 10.5802/afst.1409
LA - en
ID - AFST_2014_6_23_2_335_0
ER -
%0 Journal Article
%A Corey Dunn
%A Matthew Miller
%A Max Wakefield
%A Sebastian Zwicknagl
%T Equivalence classes of Latin squares and nets in ${\mathbb{C}P}^2$
%J Annales de la Faculté des sciences de Toulouse : Mathématiques
%D 2014
%P 335-351
%V 23
%N 2
%I Université Paul Sabatier, Institut de Mathématiques
%C Toulouse
%U https://afst.centre-mersenne.org/articles/10.5802/afst.1409/
%R 10.5802/afst.1409
%G en
%F AFST_2014_6_23_2_335_0
Corey Dunn; Matthew Miller; Max Wakefield; Sebastian Zwicknagl. Equivalence classes of Latin squares and nets in ${\mathbb{C}P}^2$. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 23 (2014) no. 2, pp. 335-351. doi : 10.5802/afst.1409. https://afst.centre-mersenne.org/articles/10.5802/afst.1409/
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