TY - JOUR
T1 - Curious bounds for floor function sums
AU - Thanatipanonda, Thotsaporn
AU - Wong, Elaine
N1 - Publisher Copyright:
© 2018, University of Waterloo. All rights reserved.
PY - 2018/1/1
Y1 - 2018/1/1
N2 - Jacobsthal was the first to study a certain kind of sum of floor functions. His work was followed by that of Carlitz, Grimson, and Tverberg. More recently, Onphaeng and Pongsriiam proved some sharp upper and lower bounds for the sums of Jacobsthal and Tverberg. In this paper, we devise concise formulas for these sums, which we then use to prove the upper and lower bounds claimed by Tverberg. Furthermore, we present conjectural lower and upper bounds for these sums.
AB - Jacobsthal was the first to study a certain kind of sum of floor functions. His work was followed by that of Carlitz, Grimson, and Tverberg. More recently, Onphaeng and Pongsriiam proved some sharp upper and lower bounds for the sums of Jacobsthal and Tverberg. In this paper, we devise concise formulas for these sums, which we then use to prove the upper and lower bounds claimed by Tverberg. Furthermore, we present conjectural lower and upper bounds for these sums.
KW - Floor function
KW - Optimization
KW - Sum
UR - http://www.scopus.com/inward/record.url?scp=85044768769&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:85044768769
SN - 1530-7638
VL - 21
JO - Journal of Integer Sequences
JF - Journal of Integer Sequences
IS - 1
M1 - 18.1.8
ER -