On the upper bound for the density of any injective vector
Prikladnaâ diskretnaâ matematika, no. 1 (2013), pp. 117-124
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In this work, the Stern's sequence $b_1 = 1,$ $b_2 = 1,$ $b_3 = 2,$ $b_4 = 3,$ $b_5 = 6,$ $b_6 = 11,$ $b_7 = 20,$ $b_8 = 40, \ldots$ is considered, and the upper and lower bounds for $b_i$
are determined. Supposing that the vector $(a_1, \ldots, a_r)$, where $r \geq 4,$
$a_1 = b_r$, $a_2 = b_r + b_{r - 1}$, $\ldots$, $a_r = \sum\limits_{i = 1}^r b_i$,
is the injective one having the least maximum element among all other injective vectors of length $r$, the upper bound for density of any injective vector
is stated.
Keywords:
density of injective vector, Stern's sequence.
@article{PDM_2013_1_a10,
author = {D. M. Murin},
title = {On the upper bound for the density of any injective vector},
journal = {Prikladna\^a diskretna\^a matematika},
pages = {117--124},
publisher = {mathdoc},
number = {1},
year = {2013},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/PDM_2013_1_a10/}
}
D. M. Murin. On the upper bound for the density of any injective vector. Prikladnaâ diskretnaâ matematika, no. 1 (2013), pp. 117-124. http://geodesic.mathdoc.fr/item/PDM_2013_1_a10/