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Research Article

Sandpile groups of Cayley graphs of 𝔽r2

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Received 06 Aug 2023, Accepted 19 Apr 2024, Published online: 15 May 2024

References

  • Anzis, B., Prasad, R. (2016). On the critical groups of cubes. http://www-users.math.umn.edu/∼reiner/REU/AnzisPrasad2016.pdf (accessed: 07.23.2018).
  • Bai, H. (2003). On the critical group of the n-cube. Linear Algebra Appl. 369:251–261. DOI: 10.1016/S0024-3795(02)00727-9.
  • Benkart, G., Klivans, C., Reiner, V. (2018). Chip firing on Dynkin diagrams and McKay quivers. Math. Zeitschrift 290:615–648.
  • Brouwer, A. E., Haemers, W. H. (2012). Spectra of Graphs. Universitext. New York: Springer.
  • Chandler, D. B., Sin, P., Xiang, Q. (2015). The Smith and critical groups of Paley graphs. J. Algebraic Combin. 41(4):1013–1022.
  • Chandler, D. B., Sin, P., Xiang, Q. (2017). The Smith group of the hypercube graph. Designs, Codes Cryptogr. 84(1–2):283–294.
  • Corry, S., Perkinson, D. (2018). Divisors and Sandpiles. Providence, RI: American Mathematical Society.
  • Ducey, J. E., Jalil, D. M. (2014). Integer invariants of abelian Cayley graphs. Linear Algebra Appl. 445:316–325. DOI: 10.1016/j.laa.2013.12.004.
  • Gaetz, C. (2016). Critical groups of group representations. Linear Algebra Appl. 508:91–99. DOI: 10.1016/j.laa.2016.07.001.
  • Grinberg, D., Huang, J., Reiner, V. (2020). Critical groups for Hopf algebra modules. Math. Proc. Cambridge Philos. Soc. 168(3):473–503.
  • Iga, K., Klivans, C., Kostiuk, J., Yuen, C. H. (2023). Eigenvalues and critical groups of Adinkras. Adv. Appl. Math. 143:Paper No. 102450, 45. DOI: 10.1016/j.aam.2022.102450.
  • Klivans, C. J. (2019). The Mathematics of Chip-Firing. Discrete Mathematics and its Applications (Boca Raton). Boca Raton, FL: CRC Press.
  • Reiner, V., Tseng, D. (2014). Critical groups of covering, voltage and signed graphs. Discrete Math. 318:10–40. DOI: 10.1016/j.disc.2013.11.008.
  • Rushanan, J. J. (1995). Eigenvalues and the Smith normal form. Linear Algebra Appl. 216:177–184. DOI: 10.1016/0024-3795(93)00131-I.
  • Stanley, R. P. (2013). Algebraic Combinatorics. Undergraduate Texts in Mathematics. New York: Springer, Walks, trees, tableaux, and more.
  • Vishnoi, N. K. (2012). Lx = b Laplacian solvers and their algorithmic applications. Found. Trends Theor. Comput. Sci. 8(1–2):front matter, 1–141 (2013).
  • Yuen, C. H. (2024). The critical groups of Adinkras up to 2-rank of Cayley graphs. Electron. J. Combin. 31(1):Paper No. 1.38, 9pp. DOI: 10.37236/11758.