Geodesic
On a Functional of the Number of Nonoverlapping Chains Appearing in the Polynomial Scheme and Its Connection with Entropy
Matematičeskie zametki, Tome 114 (2023) no. 3, pp. 390-403

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Consider $n$ independent chains consisting of $k$ independent polynomial trials with $M$ outcomes. It is assumed that $n, k \to \infty$ and $\ln(n/M^k)=o(k)$. We find the asymptotics of the normalized logarithm of the number of appearing chains and indicate the connection between this functional and the entropy.
Keywords: number of absent chains, number of empty cells, entropy, Shannon–McMillan–Breiman theorem, random allocations. 
@article{MZM_2023_114_3_a5,
     author = {M. P. Savelov},
     title = {On a {Functional} of the {Number} of {Nonoverlapping} {Chains} {Appearing} in the {Polynomial} {Scheme} and {Its} {Connection} with {Entropy}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {390--403},
     publisher = {mathdoc},
     volume = {114},
     number = {3},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2023_114_3_a5/}
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M. P. Savelov. On a Functional of the Number of Nonoverlapping Chains Appearing in the Polynomial Scheme and Its Connection with Entropy. Matematičeskie zametki, Tome 114 (2023) no. 3, pp. 390-403. http://geodesic.mathdoc.fr/item/MZM_2023_114_3_a5/