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

2019/10/22 by Patra, Asim, Panda, Gopal Krishna
#Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1910.10132

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.

Related

• Generalized Balancing and Balancing-Lucas numbers
• Additional close links between balancing and Lucas-balancing polynomials
• A generalization of carries process and Eulerian numbers
• On Generalized Balancing Sequences
• Lucas-Euler relations using balancing and Lucas-balancing polynomials