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Algebra i Analiz, 2002, Volume 14, Issue 2, Pages 11–55 (Mi aa840)  

This article is cited in 34 scientific papers (total in 34 papers)

Research Papers

Characterization of cyclotomic schemes and normal Schur rings over a cyclic group

S. A. Evdokimova, I. N. Ponomarenkob

a St. Petersburg Institute for Informatics and Automation of RAS
b St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Full text: PDF file (2562 kB)

English version:
St. Petersburg Mathematical Journal, 2003, 14:2, 189–221

Bibliographic databases:
Received: 15.10.2001

Citation: S. A. Evdokimov, I. N. Ponomarenko, “Characterization of cyclotomic schemes and normal Schur rings over a cyclic group”, Algebra i Analiz, 14:2 (2002), 11–55; St. Petersburg Math. J., 14:2 (2003), 189–221

Citation in format AMSBIB
\Bibitem{EvdPon02}
\by S.~A.~Evdokimov, I.~N.~Ponomarenko
\paper Characterization of cyclotomic schemes and normal Schur rings over a~cyclic group
\jour Algebra i Analiz
\yr 2002
\vol 14
\issue 2
\pages 11--55
\mathnet{http://mi.mathnet.ru/aa840}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1925880}
\zmath{https://zbmath.org/?q=an:1056.20001}
\transl
\jour St. Petersburg Math. J.
\yr 2003
\vol 14
\issue 2
\pages 189--221


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. A. Evdokimov, I. N. Ponomarenko, “Polynomial time recognition and verification of isomorphism of circular graphs”, St. Petersburg Math. J., 15:6 (2004), 813–835  mathnet  crossref  mathscinet  zmath
    2. S. A. Evdokimov, I. N. Ponomarenko, “On the vertex connectivity of a relation in association scheme”, J. Math. Sci. (N. Y.), 134:5 (2006), 2354–2357  mathnet  crossref  mathscinet  zmath
    3. Kovács I., “Classifying arc-transitive circulants”, J. Algebraic Combin., 20:3 (2004), 353–358  crossref  mathscinet  zmath  isi  scopus
    4. Muzychuk M., “A solution of the isomorphism problem for circulant graphs”, Proc. London Math. Soc. (3), 88:1 (2004), 1–41  crossref  mathscinet  zmath  isi  scopus
    5. Evdokimov S., Ponomarenko I., “A new look at the burnside–schur theorem”, Bulletin of the London Mathematical Society, 37:4 (2005), 535–546  crossref  mathscinet  zmath  isi  scopus
    6. Li C.H., “Permutation groups with a cyclic regular subgroup and arc transitive circulants”, Journal of Algebraic Combinatorics, 21:2 (2005), 131–136  crossref  mathscinet  zmath  isi  scopus
    7. S. A. Evdokimov, I. N. Ponomarenko, “Normal cyclotomic schemes over a finite commutative ring”, St. Petersburg Math. J., 19:6 (2008), 911–929  mathnet  crossref  mathscinet  zmath  isi
    8. S. A. Evdokimov, I. N. Ponomarenko, “Schemes of relations of the finite projective plane, and their extensions”, St. Petersburg Math. J., 21:1 (2010), 65–93  mathnet  crossref  mathscinet  zmath  isi
    9. Evdokimov S., Ponomarenko I., “Permutation group approach to association schemes”, European J. Combin., 30:6 (2009), 1456–1476  crossref  mathscinet  zmath  isi  elib  scopus
    10. Muzychuk M., Ponomarenko I., “Schur rings”, European J. Combin., 30:6 (2009), 1526–1539  crossref  mathscinet  zmath  isi  elib  scopus
    11. Praeger C. E., Xu Jing, “A note on arc-transitive circulant digraphs”, J. Group Theory, 12:1 (2009), 107–117  crossref  mathscinet  zmath  isi  scopus
    12. Dobson E., Kovacs I., “Automorphism groups of Cayley digraphs of Z(p)(3)”, Electronic Journal of Combinatorics, 16:1 (2009), R149  mathscinet  isi
    13. Muzychuk M., “A wedge product of association schemes”, European Journal of Combinatorics, 30:3 (2009), 705–715  crossref  mathscinet  zmath  isi  scopus
    14. Evdokimov S., Ponomarenko I., “Schur rings over a Galois ring of odd characteristic”, Journal of Combinatorial Theory Series A, 117:7 (2010), 827–841  crossref  mathscinet  zmath  isi  scopus
    15. Dobson E., “Asymptotic automorphism groups of Cayley digraphs and graphs of abelian groups of prime-power order”, Ars Mathematica Contemporanea, 3:2 (2010), 201–214  mathscinet  zmath  isi
    16. Kovacs I., Nedela R., “Decomposition of skew-morphisms of cyclic groups”, Ars Mathematica Contemporanea, 4:2 (2011), 329–349  mathscinet  zmath  isi
    17. Bailey R.F., Cameron P.J., “Base size, metric dimension and other invariants of groups and graphs”, Bull London Math Soc, 43:2 (2011), 209–242  crossref  mathscinet  zmath  isi  elib  scopus
    18. Muzychuk M., Ponomarenko I., “On quasi-thin association schemes”, J Algebra, 351:1 (2012), 467–489  crossref  mathscinet  zmath  isi  elib  scopus
    19. S. A. Evdokimov, I. N. Ponomarenko, “Schurity of $\mathrm S$-rings over a cyclic group and generalized wreath product of permutation groups”, St. Petersburg Math. J., 24:3 (2013), 431–460  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    20. J. Math. Sci. (N. Y.), 192:3 (2013), 316–338  mathnet  crossref  mathscinet
    21. Muzychuk M., Ponomarenko I., “On Pseudocyclic Association Schemes”, ARS Math. Contemp., 5:1 (2012), 1–25  mathscinet  zmath  isi  elib
    22. St. Petersburg Math. J., 25:5 (2014), 755–773  mathnet  crossref  mathscinet  zmath  isi  elib
    23. Arora M., Ivanyos G., Karpinski M., Saxena N., “Deterministic Polynomial Factoring and Association Schemes”, LMS J. Comput. Math., 17:1 (2014), 123–140  crossref  mathscinet  zmath  isi  elib  scopus
    24. Bhoumik S., Dobson E., Morris J., “On the Automorphism Groups of Almost All Circulant Graphs and Digraphs”, ARS Math. Contemp., 7:2 (2014), 499–518  mathscinet  zmath  isi
    25. M. Muzychuk, I. Ponomarenko, “On Schur $2$-groups”, J. Math. Sci. (N. Y.), 219:4 (2016), 565–594  mathnet  crossref  mathscinet
    26. Xu J., “Digraph Representations of 2-Closed Permutation Groups With a Normal Regular Cyclic Subgroup”, Electron. J. Comb., 22:4 (2015), P4.31  mathscinet  isi
    27. Evdokimov S. Ponomarenko I., “Coset Closure of a Circulant S-Ring and Schurity Problem”, J. Algebra. Appl., 15:4 (2016), 1650068  crossref  mathscinet  zmath  isi  elib  scopus
    28. Evdokimov S. Kovacs I. Ponomarenko I., “on Schurity of Finite Abelian Groups”, Commun. Algebr., 44:1 (2016), 101–117  crossref  mathscinet  zmath  isi  elib  scopus
    29. St. Petersburg Math. J., 28:1 (2017), 21–35  mathnet  crossref  mathscinet  isi  elib
    30. Dobson E., Spiga P., Verret G., “Cayley graphs on abelian groups”, Combinatorica, 36:4 (2016), 371–393  crossref  mathscinet  zmath  isi  scopus
    31. Ryabov G., “On Schur $p$-groups of odd order”, J. Algebra. Appl., 16:3 (2017), 1750045  crossref  mathscinet  zmath  isi  scopus
    32. Araujo J., Bentz W., Dobson E., Konieczny J., Morris J., “Automorphism Groups of Circulant Digraphs With Applications to Semigroup Theory”, Combinatorica, 38:1 (2018), 1–28  crossref  mathscinet  zmath  isi  scopus
    33. G. K. Ryabov, “Separability of Schur rings over Abelian $p$-groups”, Algebra and Logic, 57:1 (2018), 49–68  mathnet  crossref  crossref  isi
    34. Bagherian J., “On the Association Schemes With the Thin Radical Series”, J. Algebra. Appl., 18:4 (2019), 1950071  crossref  mathscinet  isi  scopus
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