TY - JOUR
T1 - Every poset has a central element
AU - Linial, Nathan
AU - Saks, Michael
N1 - Funding Information:
in part by NSF under
PY - 1985/11
Y1 - 1985/11
N2 - It is proved that there exists a constant δ, 1 2 > δ > 0, such that in every finite partially ordered set there is an element such that the fraction of order ideals containing that element is between δ and 1-δ. It is shown that δ can be taken to be at least (3-log2 5) 4≊0.17. This settles a question asked independently by Colburn and Rival, and Rosenthal. The result implies that the information-theoretic lower bound for a certain class of search problems on partially ordered sets is tight up to a multiplicative constant.
AB - It is proved that there exists a constant δ, 1 2 > δ > 0, such that in every finite partially ordered set there is an element such that the fraction of order ideals containing that element is between δ and 1-δ. It is shown that δ can be taken to be at least (3-log2 5) 4≊0.17. This settles a question asked independently by Colburn and Rival, and Rosenthal. The result implies that the information-theoretic lower bound for a certain class of search problems on partially ordered sets is tight up to a multiplicative constant.
UR - http://www.scopus.com/inward/record.url?scp=0041510901&partnerID=8YFLogxK
U2 - 10.1016/0097-3165(85)90087-1
DO - 10.1016/0097-3165(85)90087-1
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:0041510901
SN - 0097-3165
VL - 40
SP - 195
EP - 210
JO - Journal of Combinatorial Theory. Series A
JF - Journal of Combinatorial Theory. Series A
IS - 2
ER -