Original scientific paper
Some Refinements of Formulae Involving Floor and Ceiling Functions
Luka Podrug
orcid.org/0000-0002-0336-7997
; Faculty of Civil Engineering, University of Zagreb, Zagreb
Dragutin Svrtan
; Department of Mathematics, Faculty of Science, University of Zagreb, Zagreb
Abstract
The floor and ceiling functions appear often in mathematics and manipulating sums involving floors and ceilings is a subtle game. Fortunately, the well-known textbook Concrete Mathematics provides a nice introduction with a number of techniques explained and a number of single or double sums treated as exercises. For two such double sums we provide their single-sum analogues. These closed-form identities are given in terms of a dual partition of the multiset (regarded as a partition) of all b-ary digits of a nonnegative integer. We also present the double- and single-sum analogues involving the fractional part function and the shifted fractional part function.
Keywords
sum; floor function; ceiling function; fractional part function
Hrčak ID:
309006
URI
Publication date:
22.10.2023.
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