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Note on the permutation group associated to E-polynomials

Yıl 2022, Cilt: 9 Sayı: 1, 1 - 7, 15.01.2022

Hirotaka Imamura Masashi Kosuda Manabu Oura

https://doi.org/10.13069/jacodesmath.1056485

Öz

This is a continuation of our project which focuses on E-polynomials and the related combinatorics. A pair of groups appearing in the definition of E-polynomials yields the permutation group. In this paper, we determine the multi-matrix structures of the centralizer algebras of the tensor representations of this permutation group.

Anahtar Kelimeler

Centralizer algebra Permutation group Algebra

Kaynakça

  • [1] E. Bannai, T. Ito, Algebraic combinatorics I: association schemes, The Benjamin/Cummings Publishing Co, California (1984).
  • [2] W. Bosma, J. Cannon, C. Playoust, The Magma algebra system I: the user language, J. Symbolic Comput. 24(3-4) (1997) 235–265.
  • [3] M. Broué, M. Enguehard, Polynômes des poids de certains codes et fonctions thêta de certains réseaux, Ann. Sci. École Norm. Sup. 5(1) (1972) 157–181.
  • [4] W. Duke, On codes and Siegel modular forms, Internat. Math. Res. Notices 5 (1993) 125–136.
  • [5] A. Hanaki, http://math.shinshu-u.ac.jp/ hanaki/as/.
  • [6] M. Kosuda, M. Oura, On the centralizer algebras of the primitive unitary reflection group of order 96, Tokyo J. Math. 39(2) (2016) 469–482.
  • [7] M. Kosuda, M. Oura, Centralizer algebras of the group associated to Z4-codes, Discrete Math. 340(10) (2017) 2437–2446.
  • [8] T. Motomura, M. Oura, E-polynomials associated to Z_4-codes, Hokkaido Math. J. 47(2) (2018) 339–350.
  • [9] M. Oura, The dimension formula for the ring of code polynomials in genus 4, Osaka J. Math. 34(1) (1997) 53–72.
  • [10] M. Oura, Eisenstein polynomials associated to binary codes, Int. J. Number Theory 5(4) (2009) 635–640.
  • [11] M. Oura, Eisenstein polynomials associated to binary codes (II), Kochi J. Math. 11 (2016) 35–41.
  • [12] M. Oura, http://sphere.w3.kanazawa-u.ac.jp
  • [13] B. Runge, On Siegel modular forms I, J. Reine Angew. Math. 436 (1993) 57–86.
  • [14] B. Runge, On Siegel modular forms II, Nagoya Math. J. 138 (1995) 179–197.
  • [15] B. Runge, Codes and Siegel modular forms, Discrete Math. 148(1-3) (1996) 175–204.
  • [16] C. C. Sims, Graphs and finite permutation groups, Math. Z. 95 (1967) 76–86.
  • [17] H. Wielandt, Finite permutation groups, Academic Press, New York-London (1964).

Yıl 2022, Cilt: 9 Sayı: 1, 1 - 7, 15.01.2022

Hirotaka Imamura Masashi Kosuda Manabu Oura

https://doi.org/10.13069/jacodesmath.1056485

Öz

Kaynakça

  • [1] E. Bannai, T. Ito, Algebraic combinatorics I: association schemes, The Benjamin/Cummings Publishing Co, California (1984).
  • [2] W. Bosma, J. Cannon, C. Playoust, The Magma algebra system I: the user language, J. Symbolic Comput. 24(3-4) (1997) 235–265.
  • [3] M. Broué, M. Enguehard, Polynômes des poids de certains codes et fonctions thêta de certains réseaux, Ann. Sci. École Norm. Sup. 5(1) (1972) 157–181.
  • [4] W. Duke, On codes and Siegel modular forms, Internat. Math. Res. Notices 5 (1993) 125–136.
  • [5] A. Hanaki, http://math.shinshu-u.ac.jp/ hanaki/as/.
  • [6] M. Kosuda, M. Oura, On the centralizer algebras of the primitive unitary reflection group of order 96, Tokyo J. Math. 39(2) (2016) 469–482.
  • [7] M. Kosuda, M. Oura, Centralizer algebras of the group associated to Z4-codes, Discrete Math. 340(10) (2017) 2437–2446.
  • [8] T. Motomura, M. Oura, E-polynomials associated to Z_4-codes, Hokkaido Math. J. 47(2) (2018) 339–350.
  • [9] M. Oura, The dimension formula for the ring of code polynomials in genus 4, Osaka J. Math. 34(1) (1997) 53–72.
  • [10] M. Oura, Eisenstein polynomials associated to binary codes, Int. J. Number Theory 5(4) (2009) 635–640.
  • [11] M. Oura, Eisenstein polynomials associated to binary codes (II), Kochi J. Math. 11 (2016) 35–41.
  • [12] M. Oura, http://sphere.w3.kanazawa-u.ac.jp
  • [13] B. Runge, On Siegel modular forms I, J. Reine Angew. Math. 436 (1993) 57–86.
  • [14] B. Runge, On Siegel modular forms II, Nagoya Math. J. 138 (1995) 179–197.
  • [15] B. Runge, Codes and Siegel modular forms, Discrete Math. 148(1-3) (1996) 175–204.
  • [16] C. C. Sims, Graphs and finite permutation groups, Math. Z. 95 (1967) 76–86.
  • [17] H. Wielandt, Finite permutation groups, Academic Press, New York-London (1964).
Toplam 17 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Hirotaka Imamura Bu kişi benim

Masashi Kosuda Bu kişi benim 0000-0003-0028-6785

Manabu Oura Bu kişi benim 0000-0002-0498-9667

Erken Görünüm Tarihi 31 Ocak 2022
Yayımlanma Tarihi 15 Ocak 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 9 Sayı: 1

Kaynak Göster

APA Imamura, H., Kosuda, M., & Oura, M. (t.y.). Note on the permutation group associated to E-polynomials. Journal of Algebra Combinatorics Discrete Structures and Applications, 9(1), 1-7. https://doi.org/10.13069/jacodesmath.1056485
AMA Imamura H, Kosuda M, Oura M. Note on the permutation group associated to E-polynomials. Journal of Algebra Combinatorics Discrete Structures and Applications. 9(1):1-7. doi:10.13069/jacodesmath.1056485
Chicago Imamura, Hirotaka, Masashi Kosuda, ve Manabu Oura. “Note on the Permutation Group Associated to E-Polynomials”. Journal of Algebra Combinatorics Discrete Structures and Applications 9, sy. 1 t.y.: 1-7. https://doi.org/10.13069/jacodesmath.1056485.
EndNote Imamura H, Kosuda M, Oura M Note on the permutation group associated to E-polynomials. Journal of Algebra Combinatorics Discrete Structures and Applications 9 1 1–7.
IEEE H. Imamura, M. Kosuda, ve M. Oura, “Note on the permutation group associated to E-polynomials”, Journal of Algebra Combinatorics Discrete Structures and Applications, c. 9, sy. 1, ss. 1–7, doi: 10.13069/jacodesmath.1056485.
ISNAD Imamura, Hirotaka vd. “Note on the Permutation Group Associated to E-Polynomials”. Journal of Algebra Combinatorics Discrete Structures and Applications 9/1 (t.y.), 1-7. https://doi.org/10.13069/jacodesmath.1056485.
JAMA Imamura H, Kosuda M, Oura M. Note on the permutation group associated to E-polynomials. Journal of Algebra Combinatorics Discrete Structures and Applications.;9:1–7.
MLA Imamura, Hirotaka vd. “Note on the Permutation Group Associated to E-Polynomials”. Journal of Algebra Combinatorics Discrete Structures and Applications, c. 9, sy. 1, ss. 1-7, doi:10.13069/jacodesmath.1056485.
Vancouver Imamura H, Kosuda M, Oura M. Note on the permutation group associated to E-polynomials. Journal of Algebra Combinatorics Discrete Structures and Applications. 9(1):1-7.