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• W2964221473 endingPage "1332" @default.
• W2964221473 startingPage "1302" @default.
• W2964221473 abstract "Generalized Zeckendorf decompositions are expansions of integers as sums of elements of solutions to recurrence relations. The simplest cases are base-$b$ expansions, and the standard Zeckendorf decomposition uses the Fibonacci sequence. The expansions are finite sequences of nonnegative integer coefficients (satisfying certain technical conditions to guarantee uniqueness of the decomposition) and which can be viewed as analogues of sequences of variable-length words made from some fixed alphabet. In this paper we present a new approach and construction for uniform measures on expansions, identifying them as the distribution of a Markov chain conditioned not to hit a set. This gives a unified approach that allows us to easily recover results on the expansions from analogous results for Markov chains, and in this paper we focus on laws of large numbers, central limit theorems for sums of digits, and statements on gaps (zeros) in expansions. We expect the approach to prove useful in other similar contexts." @default.
• W2964221473 created "2019-07-30" @default.
• W2964221473 creator A5026810203 @default.
• W2964221473 creator A5049983178 @default.
• W2964221473 date "2016-01-01" @default.
• W2964221473 modified "2023-10-14" @default.
• W2964221473 title "A Probabilistic Approach to Generalized Zeckendorf Decompositions" @default.
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• W2964221473 doi "https://doi.org/10.1137/140996859" @default.
• W2964221473 hasPublicationYear "2016" @default.
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