2020/09/18 by Sergey Avvakumov, Avvakumov, Sergey, Roman Karasev +1 · 2 citations
Mathematics · #55M20 #55M35 #91B32 #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #Metric Geometry (math.MG) #math.AT #math.CO #math.MG #msc:55M20 #msc:55M35 #msc:91B32
paper · pdf · doi:10.48550/arxiv.2009.09862
arXiv admin note: substantial text overlap with arXiv:1804.03057
arxiv created 2022/01/04 · arxiv updated 2022/01/05
We prove that, for any positive integer m, a segment may be partitioned into m possibly degenerate or empty segments with equal values of a continuous function f of a segment, assuming that f may take positive and negative values, but its value on degenerate or empty segments is zero.