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