Geodesic
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. 
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     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/}
}
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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/