On the Growth of the Number of Determinants with Restricted Entries
Matematičeskie zametki, Tome 109 (2021) no. 6, pp. 803-809.

Voir la notice de l'article provenant de la source Math-Net.Ru

We study the problem about the number of distinct determinants of matrices with entries from a fixed set.
Keywords: sum-product phenomenon, determinants.
@article{MZM_2021_109_6_a0,
     author = {L. M. Arutyunyan},
     title = {On the {Growth} of the {Number} of {Determinants} with {Restricted} {Entries}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {803--809},
     publisher = {mathdoc},
     volume = {109},
     number = {6},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2021_109_6_a0/}
}
TY  - JOUR
AU  - L. M. Arutyunyan
TI  - On the Growth of the Number of Determinants with Restricted Entries
JO  - Matematičeskie zametki
PY  - 2021
SP  - 803
EP  - 809
VL  - 109
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2021_109_6_a0/
LA  - ru
ID  - MZM_2021_109_6_a0
ER  - 
%0 Journal Article
%A L. M. Arutyunyan
%T On the Growth of the Number of Determinants with Restricted Entries
%J Matematičeskie zametki
%D 2021
%P 803-809
%V 109
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2021_109_6_a0/
%G ru
%F MZM_2021_109_6_a0
L. M. Arutyunyan. On the Growth of the Number of Determinants with Restricted Entries. Matematičeskie zametki, Tome 109 (2021) no. 6, pp. 803-809. http://geodesic.mathdoc.fr/item/MZM_2021_109_6_a0/

[1] T. C. Tao, V. H. Vu, Additive Combinatorics, Cambridge Stud. Adv. Math., 105, Cambridge Univ. Press, Cambridge, 2006 | MR

[2] B. Murphy, G. Petridis, O. Roche-Newton, M. Rudnev, I. D. Shkredov, “New results on sum-product type growth over fields”, Mathematika, 65:3 (2019), 588–642 ; (2017), arXiv: 1702.01003 | MR

[3] D. Koh, T. Pham, C.-Y. Shen, L. A. Vinh, “On the determinants and permanents of matrices with restricted entries over prime fields”, Pacific J. Math., 300:2 (2019), 405–417 ; (2018), arXiv: 1801.03432 | MR

[4] L. A. Vinh, “Distribution of determinant of matrices with restricted entries over finite fields”, J. Comb. Number Theory, 1:3 (2010), 203–212 | MR

[5] O. Ahmadi, I. E. Shparlinski, “Distribution of matrices with restricted entries over finite fields”, Indag. Math. (N.S.), 18:3 (2007), 327–337 | DOI | MR

[6] A. Greenleaf, A. Iosevich, M. Mourgoglou, “On volumes determined by subsets of Euclidean space”, Forum Math., 27:1 (2015), 635–646 ; (2011), arXiv: 1110.6790 | MR

[7] D. Covert, D. Hart, A. Iosevich, D. Koh, M. Rudnev, “Generalized incidence theorems, homogeneous forms and sum-product estimates in finite fields”, European J. Combin, 31:1 (2010), 306–319 | DOI | MR

[8] M. Rudnev, “On the number of incidences between planes and points in three dimensions”, Combinatorica, 38:1 (2018), 219–254 | DOI | MR

[9] A. A. Glibichuk, S. V. Konyagin, “Additive properties of product sets in fields of prime order”, Additive Combinatorics, CRM Proc. Lecture Notes, 43, Amer. Math. Soc., Providence, RI, 2007, 279–286 | MR

[10] L. A. Vinh, “On the permanents of matrices with restricted entries over finite fields”, SIAM J. Discrete Math., 26:3 (2012), 997–1007 | DOI | MR

[11] A. A. Glibichuk, “Summy stepenei podmnozhestv proizvolnogo konechnogo polya”, Izv. RAN. Ser. matem., 75:2 (2011), 35–68 | DOI | MR | Zbl