Geodesic
Combinatorial properties of flat sections of the generalized Pascal's pyramid and construction of navigation routes
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, Geometry, and Combinatorics, Tome 214 (2022), pp. 53-59

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The article describes the methods of the mathematical apparatus of hierarchical structures. The definition of the generalized Pascal pyramid is given and the sums of the elements of its flat sections are considered. Recurrence relations that these sums satisfy, as well as enumerative interpretations of the combinatorial objects under study are shown. Combinatorial paths on integer lattices and the use of recurrence relations to estimate the number of deviations of the trajectory of an unmanned aerial vehicle from a given motion vector are described.
Keywords: combinatorial analysis, generalized Pascal's pyramid, recurrent property, integer lattice, trajectory.
Mots-clés : Pascal's triangle 
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     author = {O. V. Kuz'min and B. A. Starkov},
     title = {Combinatorial properties of flat sections of the generalized {Pascal's} pyramid and construction of navigation routes},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {53--59},
     publisher = {mathdoc},
     volume = {214},
     year = {2022},
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     url = {http://geodesic.mathdoc.fr/item/INTO_2022_214_a5/}
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O. V. Kuz'min; B. A. Starkov. Combinatorial properties of flat sections of the generalized Pascal's pyramid and construction of navigation routes. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, Geometry, and Combinatorics, Tome 214 (2022), pp. 53-59. http://geodesic.mathdoc.fr/item/INTO_2022_214_a5/