Geodesic
On the distribution of the number of ones in a Boolean Pascal's triangle
Diskretnaya Matematika, Tome 18 (2006) no. 2, pp. 123-131

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

This research is devoted to estimating the number of Boolean Pascal's triangles of large enough size $s$ containing a given number of ones $\xi\le ks$, $k>0$. We demonstrate that any such Pascal's triangle contains a zero triangle whose size differs from $s$ by at most constant depending only on $k$. We prove that there is a monotone unbounded sequence of rational numbers $0=k_0$ such that the distribution of the number of triangles is concentrated in some neighbourhoods of the points $k_is$. The form of the distribution in each neighbourhood depends not on $s$ but on the residue of $s$ some modulo depending on $i\ge 0$. 
@article{DM_2006_18_2_a8,
     author = {F. M. Malyshev and E. V. Kutyreva},
     title = {On the distribution of the number of ones in a {Boolean} {Pascal's} triangle},
     journal = {Diskretnaya Matematika},
     pages = {123--131},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2006_18_2_a8/}
}
TY  - JOUR
AU  - F. M. Malyshev
AU  - E. V. Kutyreva
TI  - On the distribution of the number of ones in a Boolean Pascal's triangle
JO  - Diskretnaya Matematika
PY  - 2006
SP  - 123
EP  - 131
VL  - 18
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DM_2006_18_2_a8/
LA  - ru
ID  - DM_2006_18_2_a8
ER  - 
%0 Journal Article
%A F. M. Malyshev
%A E. V. Kutyreva
%T On the distribution of the number of ones in a Boolean Pascal's triangle
%J Diskretnaya Matematika
%D 2006
%P 123-131
%V 18
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DM_2006_18_2_a8/
%G ru
%F DM_2006_18_2_a8
F. M. Malyshev; E. V. Kutyreva. On the distribution of the number of ones in a Boolean Pascal's triangle. Diskretnaya Matematika, Tome 18 (2006) no. 2, pp. 123-131. http://geodesic.mathdoc.fr/item/DM_2006_18_2_a8/