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arXiv · 1910.10132

Appearance of Balancing and related number sequences in steady state probabilities of some Markov chains

Asim Patra·Gopal Krishna Panda
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Abstract

Balancing and Lucas-balancing numbers are solutions of a Diophantine equation and satisfy a second order homogeneous recurrence relation. Interestingly, these numbers can be seen as numerators and denominators in the steady state probabilities of a class of transition probability matrices of Markov chains. An identity relating the balancing numbers and the silver ratio can be obtained as a byproduct.

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Asim Patra, Gopal Krishna Panda. 2019-10-22. Appearance of Balancing and related number sequences in steady state probabilities of some Markov chains. https://arxiv.org/abs/1910.10132

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