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Commutative Schur rings over symmetric groups II: The case n = 6

Cilt: 3 Sayı: 2 15 Mayıs 2016
  • Amanda E. Francis
  • Stephen P. Humphries
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Commutative Schur rings over symmetric groups II: The case n = 6

Öz

We determine the commutative Schur rings over $S_6$ that contain the sum of all the transpositions in $S_6$. There are eight such types (up to conjugacy), of which four have the set of all the transpositions as a principal set of the Schur ring.

Anahtar Kelimeler

Kaynakça

  1. [1] W. Bosma, J. Cannon, Magma handbook, University of Sydney, 1993.
  2. [2] C. W. Curtis, Pioneers of Representation Theory: Frobenius, Burnside, Schur, and Brauer. Vol. 15. American Mathematical Soc., 1999.
  3. [3] S. A. Evdokimov, I. N. Ponomarenko, On a family of Schur rings over a finite cyclic group (Russian), Algebra i Analiz. 13(3) (2001) 139–154; translation in St. Petersburg Math. J. 13(3) (2002) 441–451.
  4. [4] S. P. Humphries, Commutative Schur rings over symmetric groups, J. Algebraic Combin. 42(4) (2015) 971–997.
  5. [5] S. P. Humphries, K. W. Johnson, A. Misseldine, Commutative Schur rings of maximal dimension, Comm. Algebra. 43(12) (2015) 5298–5327.
  6. [6] K. H. Leung, S. H. Man, On Schur rings over cyclic groups, Israel J. Math. 106(1) (1998) 251–267.
  7. [7] K. H. Leung, S. H. Man, On Schur rings over cyclic groups, II, J. Algebra. 183(2) (1996) 273–285.
  8. [8] M. E. Muzychuk, On the structure of basic sets of Schur rings over cyclic groups, J. Algebra. 169(2) (1994) 655–678.

Ayrıntılar

Birincil Dil

İngilizce

Konular

Mühendislik

Bölüm

Araştırma Makalesi

Yazarlar

Amanda E. Francis Bu kişi benim

Stephen P. Humphries Bu kişi benim

Yayımlanma Tarihi

15 Mayıs 2016

Gönderilme Tarihi

5 Eylül 2015

Kabul Tarihi

-

Yayımlandığı Sayı

Yıl 2016 Cilt: 3 Sayı: 2

Kaynak Göster

APA
Francis, A. E., & Humphries, S. P. (2016). Commutative Schur rings over symmetric groups II: The case n = 6. Journal of Algebra Combinatorics Discrete Structures and Applications, 3(2), 61-80. https://doi.org/10.13069/jacodesmath.79635
AMA
1.Francis AE, Humphries SP. Commutative Schur rings over symmetric groups II: The case n = 6. Journal of Algebra Combinatorics Discrete Structures and Applications. 2016;3(2):61-80. doi:10.13069/jacodesmath.79635
Chicago
Francis, Amanda E., ve Stephen P. Humphries. 2016. “Commutative Schur rings over symmetric groups II: The case n = 6”. Journal of Algebra Combinatorics Discrete Structures and Applications 3 (2): 61-80. https://doi.org/10.13069/jacodesmath.79635.
EndNote
Francis AE, Humphries SP (01 Mayıs 2016) Commutative Schur rings over symmetric groups II: The case n = 6. Journal of Algebra Combinatorics Discrete Structures and Applications 3 2 61–80.
IEEE
[1]A. E. Francis ve S. P. Humphries, “Commutative Schur rings over symmetric groups II: The case n = 6”, Journal of Algebra Combinatorics Discrete Structures and Applications, c. 3, sy 2, ss. 61–80, May. 2016, doi: 10.13069/jacodesmath.79635.
ISNAD
Francis, Amanda E. - Humphries, Stephen P. “Commutative Schur rings over symmetric groups II: The case n = 6”. Journal of Algebra Combinatorics Discrete Structures and Applications 3/2 (01 Mayıs 2016): 61-80. https://doi.org/10.13069/jacodesmath.79635.
JAMA
1.Francis AE, Humphries SP. Commutative Schur rings over symmetric groups II: The case n = 6. Journal of Algebra Combinatorics Discrete Structures and Applications. 2016;3:61–80.
MLA
Francis, Amanda E., ve Stephen P. Humphries. “Commutative Schur rings over symmetric groups II: The case n = 6”. Journal of Algebra Combinatorics Discrete Structures and Applications, c. 3, sy 2, Mayıs 2016, ss. 61-80, doi:10.13069/jacodesmath.79635.
Vancouver
1.Amanda E. Francis, Stephen P. Humphries. Commutative Schur rings over symmetric groups II: The case n = 6. Journal of Algebra Combinatorics Discrete Structures and Applications. 01 Mayıs 2016;3(2):61-80. doi:10.13069/jacodesmath.79635