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Zapiski Nauchnykh Seminarov POMI, 2002, Volume 289, Pages 207–213 (Mi znsl1603)  
This article is cited in 1 scientific paper (total in 1 paper)

Rings associated to finite projective planes and thier isomorphisms

S. A. Evdokimovab, I. N. Ponomarenkoa

a St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
b St. Petersburg Institute for Informatics and Automation of RAS
Full-text PDF (159 kB) Citations (1)
Abstract: In this paper we announce an explicit form of the standard basis of the 2-extended ring associated to the cellular ring generated by the incidence graph of a finite projective plane.This enables us to find the first example of a distance-regular graph satisfying the 6-condition which is not a distance-transivite one. One more corollary of the result obtained is that the cellular rings of any two projective planes of the same order are 2-isomorphic. This implies that if there exist at least two nonisomorphic and nondual to each other projective planes of a given order, then the separability number of any projective plane of this order is greater or equal to 3 and, moreover, it is equal to 3 for a Galois plane.
Received: 13.11.2002
English version:
Journal of Mathematical Sciences (New York), 2004, Volume 124, Issue 1, Pages 4792–4795
DOI: https://doi.org/10.1023/B:JOTH.0000042314.90723.7a
Bibliographic databases:
UDC: 512.5+512.6
Language: Russian
Citation: S. A. Evdokimov, I. N. Ponomarenko, “Rings associated to finite projective planes and thier isomorphisms”, Problems in the theory of representations of algebras and groups. Part 9, Zap. Nauchn. Sem. POMI, 289, POMI, St. Petersburg, 2002, 207–213; J. Math. Sci. (N. Y.), 124:1 (2004), 4792–4795
Citation in format AMSBIB
\Bibitem{EvdPon02}
\by S.~A.~Evdokimov, I.~N.~Ponomarenko
\paper Rings associated to finite projective planes and thier isomorphisms
\inbook Problems in the theory of representations of algebras and groups. Part~9
\serial Zap. Nauchn. Sem. POMI
\yr 2002
\vol 289
\pages 207--213
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl1603}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1949741}
\zmath{https://zbmath.org/?q=an:1069.51002}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2004
\vol 124
\issue 1
\pages 4792--4795
\crossref{https://doi.org/10.1023/B:JOTH.0000042314.90723.7a}
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  • https://www.mathnet.ru/eng/znsl/v289/p207
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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