Expanding phenomena over matrix rings

References

[1] N. Alon and J. H. Spencer, The Probabilistic Method, 3rd ed., John Wiley & Sons, Hoboken, 2008. 10.1002/9780470277331Suche in Google Scholar

[2] L. Babai, N. Nikolov and L. Pyber, Product growth and mixing in finite groups, Proceedings of the Nineteenth Annual ACM-SIAM Symposium on Discrete Algorithms, ACM, New York (2008), 248–257. Suche in Google Scholar

[3] M. Bennett, D. Hart, A. Iosevich, J. Pakianathan and M. Rudnev, Group actions and geometric combinatorics in 𝔽qd, Forum Math. 29 (2017), no. 1, 91–110. 10.1515/forum-2015-0251Suche in Google Scholar

[4] M.-C. Chang, Additive and multiplicative structure in matrix spaces, Combin. Probab. Comput. 16 (2007), no. 2, 219–238. 10.1017/S0963548306008145Suche in Google Scholar

[5] G. Chris and G. F. Royle, Algebraic Graph Theory, Grad. Texts in Math. 207, Springer, New York, 2013. Suche in Google Scholar

[6] R. Ferguson, C. Hoffman, F. Luca, A. Ostafe and I. E. Shparlinski, Some additive combinatorics problems in matrix rings, Rev. Mat. Complut. 23 (2010), no. 2, 501–513. 10.1007/s13163-010-0029-4Suche in Google Scholar

[7] D. Hart and A. Iosevich, Sums and products in finite fields: An integral geometric viewpoint, Radon Transforms, Geometry, and Wavelets, Contemp. Math. 464, American Mathematical Society, Providence (2008), 129–135. 10.1090/conm/464/09080Suche in Google Scholar

[8] D. Hart, A. Iosevich and J. Solymosi, Sum-product estimates in finite fields via Kloosterman sums, Int. Math. Res. Not. IMRN 2007 (2007), no. 5, Article ID rnm007. 10.1093/imrn/rnm007Suche in Google Scholar

[9] D. Hart, L. Li and C.-Y. Shen, Fourier analysis and expanding phenomena in finite fields, Proc. Amer. Math. Soc. 141 (2013), no. 2, 461–473. 10.1090/S0002-9939-2012-11338-3Suche in Google Scholar

[10] N. Hegyvári and F. Hennecart, Expansion for cubes in the Heisenberg group, Forum Math. 30 (2018), no. 1, 227–236. 10.1515/forum-2015-0230Suche in Google Scholar

[11] Y. D. Karabulut, Cayley digraphs of matrix rings over finite fields, to appear in Forum Math. Suche in Google Scholar

[12] D. Koh, T. Pham, C.-Y. Shen and A. V. Le, Expansion for the product of matrices in groups, Forum Math. 31 (2019), no. 1, 35–48. 10.1515/forum-2018-0063Suche in Google Scholar

[13] T. Pham, L. A. Vinh and F. De Zeeuw, Three-variable expanding polynomials and higher-dimensional distinct distances, Combinatorica (2017), 10.1007/s00493-017-3773-y. 10.1007/s00493-017-3773-ySuche in Google Scholar

[14] M. Rudnev, I. Shkredov and S. Stevens, On the energy variant of the sum-product conjecture, to appear in Rev. Mat. Iberoam. 10.4171/rmi/1126Suche in Google Scholar

[15] M. Russell, Multilinear Algebra, Algebra Logic Appl. 8, Gordon & Breach, Langhorne, 1997. Suche in Google Scholar

[16] I. E. Shparlinski, On the solvability of bilinear equations in finite fields, Glasg. Math. J. 50 (2008), no. 3, 523–529. 10.1017/S0017089508004382Suche in Google Scholar

[17] J. Solymosi, Incidences and the spectra of graphs, Combinatorial Number Theory and Additive Group Theory, Adv. Courses Math. CRM Barcelona, Birkhäuser, Basel (2009), 299–314. 10.1007/978-3-7643-8962-8_22Suche in Google Scholar

[18] J. Solymosi and T. Tao, An incidence theorem in higher dimensions, Discrete Comput. Geom. 48 (2012), no. 2, 255–280. 10.1007/s00454-012-9420-xSuche in Google Scholar

[19] T. Tao, Expanding polynomials over finite fields of large characteristic, and a regularity lemma for definable sets, Contrib. Discrete Math. 10 (2015), no. 1, 22–98. Suche in Google Scholar

[20] L. A. Vinh, On the permanents of matrices with restricted entries over finite fields, SIAM J. Discrete Math. 26 (2012), no. 3, 997–1007. 10.1137/110835050Suche in Google Scholar

[21] L. A. Vinh, On four-variable expanders in finite fields, SIAM J. Discrete Math. 27 (2013), no. 4, 2038–2048. 10.1137/120892015Suche in Google Scholar

[22] V. H. Vu, Sum-product estimates via directed expanders, Math. Res. Lett. 15 (2008), no. 2, 375–388. 10.4310/MRL.2008.v15.n2.a14Suche in Google Scholar