Rows of Pascal's triangle modulo a~prime
Diskretnyj analiz i issledovanie operacij, Tome 20 (2013) no. 2, pp. 26-46.

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

Properties of a special class of matrices arising in study of distribution of binomial coefficients modulo a prime are given. Formulas for binomial coefficients modulo a prime in the rows of Pascal's triangle are obtained. Ill. 1, bibliogr. 7.
Mots-clés : Pascal's triangle, latin matrix, binomial coefficients, modulo a prime.
@article{DA_2013_20_2_a2,
     author = {V. V. Karachik},
     title = {Rows of {Pascal's} triangle modulo a~prime},
     journal = {Diskretnyj analiz i issledovanie operacij},
     pages = {26--46},
     publisher = {mathdoc},
     volume = {20},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2013_20_2_a2/}
}
TY  - JOUR
AU  - V. V. Karachik
TI  - Rows of Pascal's triangle modulo a~prime
JO  - Diskretnyj analiz i issledovanie operacij
PY  - 2013
SP  - 26
EP  - 46
VL  - 20
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DA_2013_20_2_a2/
LA  - ru
ID  - DA_2013_20_2_a2
ER  - 
%0 Journal Article
%A V. V. Karachik
%T Rows of Pascal's triangle modulo a~prime
%J Diskretnyj analiz i issledovanie operacij
%D 2013
%P 26-46
%V 20
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DA_2013_20_2_a2/
%G ru
%F DA_2013_20_2_a2
V. V. Karachik. Rows of Pascal's triangle modulo a~prime. Diskretnyj analiz i issledovanie operacij, Tome 20 (2013) no. 2, pp. 26-46. http://geodesic.mathdoc.fr/item/DA_2013_20_2_a2/

[1] Karachik V. V., “Svoistva nopmalizovannykh $p$-latinskikh matpits”, Probl. informatiki i energetiki, 1992, no. 5–6, 9–14 | Zbl

[2] Bondarenko B. A., Generalized Pascal triangles and pyramids: their fractals, graphs and applications, The Fibonacci Association, Santa Clara, 1993, 253 pp. | Zbl

[3] Denes J., Keedwell A. D., Latin squares and their applications, Akad. Kiado, Budapest, 1974, 547 pp. | MR | Zbl

[4] Hexel E., Sachs H., “Counting residues modulo a prime in Pascal's triangle”, Indian J. Math., 20:2 (1978), 91–105 | MR | Zbl

[5] Karachik V. V., Bondarenko B. A., “Distribution of Eulerian and Stirling numbers $\bmod\,m$ in arithmetical triangles”, Vopposy vychisl. i ppikl. matematiki, 102, 1996, 133–140 | MR | Zbl

[6] Karachik V. V., “$p$-Latin matrices and Pascal's triangle modulo a prime”, Fibonacci Quarterly, 34:4 (1996), 362–372 | MR | Zbl

[7] Lucas E., “Théorie des fonctions numériques simplement périodiques”, Amer. J. Math., 1:2 (1878), 184–196 | MR