MULTI-BASE REPRESENTATIONS OF INTEGERS: ASYMPTOTIC ENUMERATION AND CENTRAL LIMIT THEOREMS

作者：Krenn Daniel^*; Ralaivaosaona Dimbinaina; Wagner Stephan

来源：Applicable Analysis and Discrete Mathematics, 2015, 9(2): 285-312.

DOI：10.2298/AADM150917018K

• Multi-base representations
• asymptotic formula
• partitions
• central limit theorem

In a multi-base representation, in contrast to the common b-ary representation, the base is replaced by products of powers of single bases. The resulting numeral system has desirable properties for fast arithmetic. It is usually redundant, meaning that each integer can have multiple different digit expansions. We provide a general asymptotic formula for the number of multi-base representations of a positive integer. Moreover, we prove central limit theorems for different statistics associated to a multi-base representation.

• 出版日期2015-10