@article{2013a,
title = {On the existence of equitable cake divisions},
author = {Katarína Cechlárová and Jozef Doboš and Eva Pillárová},
url = {http://dx.doi.org/10.1016/j.ins.2012.11.024},
issn = {0020-0255},
year = {2013},
date = {2013-01-31},
journal = {Information Sciences},
volume = {228},
pages = {239–245},
abstract = {Let the cake be represented by the unit interval and let each player have a valuation expressed by a nonatomic robability measure. A cake division is said to be equitable if the value of the piece assigned to a player by his measure is the same for all players. We show that for any number n of players in any order an equitable division xists, giving each player a contiguous cake piece. Moreover, there is at least one order in which the common value is not smaller than 1/n.},
keywords = {real functions}
}
Let the cake be represented by the unit interval and let each player have a valuation expressed by a nonatomic robability measure. A cake division is said to be equitable if the value of the piece assigned to a player by his measure is the same for all players. We show that for any number n of players in any order an equitable division xists, giving each player a contiguous cake piece. Moreover, there is at least one order in which the common value is not smaller than 1/n.
@techreport{2011,
title = {On the existence of equitable cake divisions},
author = {Katarína Cechlárová and Jozef Doboš and Eva Pillárová},
url = {http://web.science.upjs.sk/jozefdobos/wp-content/uploads/2012/02/2011.pdf},
year = {2011},
date = {2011-02-01},
number = {4},
address = {Jesenná 5, 040 01 Košice, Slovakia},
institution = {Institute of Mathematics, Faculty of Science, P J Šafárik University},
keywords = {real functions}
}
@inbook{TBB,
title = {Extrema (Appendix on extremal problems for realvalued functions of two variables)},
author = {Jozef Doboš},
url = {http://classicalrealanalysis.info/documents/PagesfromTBB-Appendix-Extrema-June7-20081.pdf},
year = {2008},
date = {2008-02-01},
booktitle = {CLASSICALREALANALYSIS.INFO},
keywords = {real functions}
}