| Title:
|
Steiner forms (English) |
| Author:
|
Hora, Jan |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
57 |
| Issue:
|
4 |
| Year:
|
2016 |
| Pages:
|
527-536 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A trilinear alternating form on dimension $n$ can be defined based on a Steiner triple system of order $n$. We prove some basic properties of these forms and using the radical polynomial we show that for dimensions up to $15$ nonisomorphic Steiner triple systems provide nonequivalent forms over $GF(2)$. Finally, we prove that Steiner triple systems of order $n$ with different number of subsystems of order $(n-1)/2$ yield nonequivalent forms over $GF(2)$. (English) |
| Keyword:
|
trilinear alternating form |
| Keyword:
|
Steiner triple system |
| Keyword:
|
radical polynomial |
| MSC:
|
15A69 |
| idZBL:
|
Zbl 06674894 |
| idMR:
|
MR3583304 |
| DOI:
|
10.14712/1213-7243.2015.182 |
| . |
| Date available:
|
2017-01-09T22:17:39Z |
| Last updated:
|
2019-01-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145947 |
| . |
| Reference:
|
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| Reference:
|
[2] Gurevich G.B.: Foundations of the Theory of Algebraic Invariants.P. Noordhoff Ltd., Groningen, 1964. Zbl 0128.24601, MR 0183733 |
| Reference:
|
[3] Djokovic D.: Classification of trivectors of an eight dimensional real vector space.Linear Multilinear Algebra 13 (1983), no. 3, 3–39. Zbl 0515.15011, MR 0691457, 10.1080/03081088308817501 |
| Reference:
|
[4] Noui L.: Transvecteur de rang $8$ sur un corps algébriquement clos.C.R. Acad. Sci. Paris Sér. I Math. 324 (1997), 611–614. Zbl 0872.15023, MR 1447029, 10.1016/S0764-4442(97)86976-5 |
| Reference:
|
[5] Colbourn C.J., Rosa A.: Triple Systems.Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1999. Zbl 1030.05017, MR 1843379 |
| Reference:
|
[6] Hora J.: Orthogonal decompositions and canonical embeddings of multilinear alternating forms.Linear Multilinear Algebra 52 (2004), no. 2, 121–132. Zbl 1049.15022, MR 2033133, 10.1080/03081080310001606517 |
| Reference:
|
[7] Hora J., Pudlák P.: Classification of $8$-dimensional trilinear alternating forms over $GF(2)$.Comm. Algebra 43 (2015), no. 8, 3459–3471. MR 3354103 |
| . |
