TY - JOUR
T1 - On the influences of variables on boolean functions in product spaces
AU - Keller, Nathan
PY - 2011/1
Y1 - 2011/1
N2 - In this paper we consider the influences of variables on Boolean functions in general product spaces. Unlike the case of functions on the discrete cube, where there is a clear definition of influence, in the general case several definitions have been presented in different papers. We propose a family of definitions for the influence that contains all the known definitions, as well as other natural definitions, as special cases. We show that the proofs of the BKKKL theorem and of other results can be adapted to our new definition. The adaptation leads to generalizations of these theorems, which are tight in terms of the definition of influence used in the assertion.
AB - In this paper we consider the influences of variables on Boolean functions in general product spaces. Unlike the case of functions on the discrete cube, where there is a clear definition of influence, in the general case several definitions have been presented in different papers. We propose a family of definitions for the influence that contains all the known definitions, as well as other natural definitions, as special cases. We show that the proofs of the BKKKL theorem and of other results can be adapted to our new definition. The adaptation leads to generalizations of these theorems, which are tight in terms of the definition of influence used in the assertion.
UR - http://www.scopus.com/inward/record.url?scp=78650420132&partnerID=8YFLogxK
U2 - 10.1017/S0963548310000234
DO - 10.1017/S0963548310000234
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AN - SCOPUS:78650420132
SN - 0963-5483
VL - 20
SP - 83
EP - 102
JO - Combinatorics Probability and Computing
JF - Combinatorics Probability and Computing
IS - 1
ER -