TY - JOUR
T1 - Edge-isoperimetric inequalities and influences
AU - Falik, Dvir
AU - Samorodnitsky, Alex
PY - 2007/9
Y1 - 2007/9
N2 - We give a combinatorial proof of the result of Kahn, Kalai and Linial [16], which states that every balanced boolean function on the n-dimensional boolean cube has a variable with influence of at least Ω(logn/n) The methods of the proof are then used to recover additional isoperimetric results for the cube, with improved constants. We also state some conjectures about optimal constants.
AB - We give a combinatorial proof of the result of Kahn, Kalai and Linial [16], which states that every balanced boolean function on the n-dimensional boolean cube has a variable with influence of at least Ω(logn/n) The methods of the proof are then used to recover additional isoperimetric results for the cube, with improved constants. We also state some conjectures about optimal constants.
UR - http://www.scopus.com/inward/record.url?scp=35348843588&partnerID=8YFLogxK
U2 - 10.1017/S0963548306008340
DO - 10.1017/S0963548306008340
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:35348843588
SN - 0963-5483
VL - 16
SP - 693
EP - 712
JO - Combinatorics Probability and Computing
JF - Combinatorics Probability and Computing
IS - 5
ER -