2013/06/11 by Prapanpong Pongsriiam, Pongsriiam, Prapanpong
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT
paper · pdf · doi:10.48550/arxiv.1306.2529
arxiv created 2013/06/11 · arxiv updated 2013/06/12
Four functions counting the number of subsets of \1, 2, ..., n\ having particular properties are defined by Nathanson and generalized by many authors. They derive explicit formulas for all four functions. In this paper, we point out that we need to compute only one of them as the others will follow as a consequence. Moreover, our method is simpler and leads to more general results than those in the literature.