Geodesic
Combinatorics associated with inflections and bitangents of plane quartics
Izvestiya. Mathematics , Tome 77 (2013) no. 4, pp. 675-695

Voir la notice de l'article provenant de la source Math-Net.Ru

After a preliminary survey and a description of some small Steiner systems from the standpoint of the theory of invariants of binary forms, we construct a binary Golay code (of length 24) using ideas from J. Grassmann's thesis of 1875. One of our tools is a pair of disjoint Fano planes. Another application of such pairs and properties of plane quartics is a construction of a new block design on 28 objects. This block design is a part of a dissection of the set of 288 Aronhold sevens. The dissection distributes the Aronhold sevens into 8 disjoint block designs of this type.
Keywords: binary form, point of inflection, plane quartic, Aronhold seven, block design, Fano plane, Steiner system, Golay code.
Mots-clés : invariant, bitangent 
@article{IM2_2013_77_4_a2,
     author = {M. Kh. Gizatullin},
     title = {Combinatorics associated with inflections and bitangents of plane quartics},
     journal = {Izvestiya. Mathematics },
     pages = {675--695},
     publisher = {mathdoc},
     volume = {77},
     number = {4},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2013_77_4_a2/}
}
TY  - JOUR
AU  - M. Kh. Gizatullin
TI  - Combinatorics associated with inflections and bitangents of plane quartics
JO  - Izvestiya. Mathematics 
PY  - 2013
SP  - 675
EP  - 695
VL  - 77
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2013_77_4_a2/
LA  - en
ID  - IM2_2013_77_4_a2
ER  - 
%0 Journal Article
%A M. Kh. Gizatullin
%T Combinatorics associated with inflections and bitangents of plane quartics
%J Izvestiya. Mathematics 
%D 2013
%P 675-695
%V 77
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2013_77_4_a2/
%G en
%F IM2_2013_77_4_a2
M. Kh. Gizatullin. Combinatorics associated with inflections and bitangents of plane quartics. Izvestiya. Mathematics , Tome 77 (2013) no. 4, pp. 675-695. http://geodesic.mathdoc.fr/item/IM2_2013_77_4_a2/