메뉴 건너뛰기




Volumn 40, Issue 4, 2012, Pages 399-424

Entropy and set cardinality inequalities for partition-determined functions

Author keywords

Additive combinatorics; Cardinality inequalities; Entropy inequalities; Sumsets

Indexed keywords


EID: 84860899256     PISSN: 10429832     EISSN: 10982418     Source Type: Journal    
DOI: 10.1002/rsa.20385     Document Type: Article
Times cited : (51)

References (34)
  • 2
    • 84860913368 scopus 로고    scopus 로고
    • Reverse Brunn-Minkowski and reverse entropy power inequalities for convex measures
    • S. Bobkov, M. Madiman, Reverse Brunn-Minkowski and reverse entropy power inequalities for convex measures, J Funct Anal, to appear.
    • J Funct Anal, to appear
    • Bobkov, S.1    Madiman, M.2
  • 3
    • 79551480856 scopus 로고    scopus 로고
    • Dimensional behaviour of entropy and information
    • S. Bobkov, M. Madiman, Dimensional behaviour of entropy and information, C R Acad Sci Paris Sér I Math 349 (2011), 201-204.
    • (2011) C R Acad Sci Paris Sér I Math , vol.349 , pp. 201-204
    • Bobkov, S.1    Madiman, M.2
  • 5
    • 84959741159 scopus 로고
    • Projections of bodies and hereditary properties of hypergraphs
    • B. Bollobás, A. Thomason, Projections of bodies and hereditary properties of hypergraphs, Bull London Math Soc 27 (1995), 417-424.
    • (1995) Bull London Math Soc , vol.27 , pp. 417-424
    • Bollobás, B.1    Thomason, A.2
  • 8
    • 10044245742 scopus 로고    scopus 로고
    • Hypergraphs, entropy, and inequalities
    • E. Friedgut, Hypergraphs, entropy, and inequalities, The American Mathematical Monthly 111 (2004), 749-760.
    • (2004) The American Mathematical Monthly , vol.111 , pp. 749-760
    • Friedgut, E.1
  • 9
    • 0018020371 scopus 로고
    • Polymatroidal dependence structure of a set of random variables
    • S. Fujishige, Polymatroidal dependence structure of a set of random variables, Information Control 39 (1978), 55-72.
    • (1978) Information Control , vol.39 , pp. 55-72
    • Fujishige, S.1
  • 10
    • 79955088672 scopus 로고    scopus 로고
    • Combinatorial number theory and additive group theory
    • Birkhäuser Verlag, Basel, Courses and seminars from the DocCourse in Combinatorics and Geometry held in Barcelona, 2008.
    • A. Geroldinger, I. Z. Ruzsa, Combinatorial number theory and additive group theory, Advanced Courses in Mathematics, CRM Barcelona, Birkhäuser Verlag, Basel, 2009. Courses and seminars from the DocCourse in Combinatorics and Geometry held in Barcelona, 2008.
    • (2009) Advanced Courses in Mathematics, CRM Barcelona
    • Geroldinger, A.1    Ruzsa, I.Z.2
  • 11
    • 77956820477 scopus 로고    scopus 로고
    • A superadditivity and submultiplicativity property for cardinalities of sumsets
    • K. Gyarmati, M. Matolcsi, I. Z. Ruzsa, A superadditivity and submultiplicativity property for cardinalities of sumsets, Combinatorica 30 (2010), 163-174.
    • (2010) Combinatorica , vol.30 , pp. 163-174
    • Gyarmati, K.1    Matolcsi, M.2    Ruzsa, I.Z.3
  • 12
    • 79960171350 scopus 로고    scopus 로고
    • Plünnecke's inequality for different summands
    • M. Grötschel, G. O. H. Katona (Editors), Springer, Berlin
    • K. Gyarmati, M. Matolcsi, I. Z. Ruzsa, Plünnecke's inequality for different summands, Building bridges, volume 19 of Bolyai Soc. Math. Stud., M. Grötschel, G. O. H. Katona (Editors), Springer, Berlin, 2008, pp. 309-320.
    • (2008) Building bridges, volume 19 of Bolyai Soc. Math. Stud. , pp. 309-320
    • Gyarmati, K.1    Matolcsi, M.2    Ruzsa, I.Z.3
  • 13
    • 0001049514 scopus 로고
    • Nonnegative entropy measures of multivariate symmetric correlations
    • T. S. Han, Nonnegative entropy measures of multivariate symmetric correlations, Information Control 36 (1978), 133-156.
    • (1978) Information Control , vol.36 , pp. 133-156
    • Han, T.S.1
  • 14
    • 0000220740 scopus 로고
    • Random walks on discrete groups: boundary and entropy
    • V. A. Kaǐmanovich, A. M. Vershik, Random walks on discrete groups: boundary and entropy, Ann Probab 11 (1983), 457-490.
    • (1983) Ann Probab , vol.11 , pp. 457-490
    • Kaǐmanovich, V.A.1    Vershik, A.M.2
  • 15
    • 51849121580 scopus 로고    scopus 로고
    • On the entropy of sums, Proc. IEEE Inform Theory Workshop, Porto, Portugal
    • M. Madiman, On the entropy of sums, Proc. IEEE Inform Theory Workshop, Porto, Portugal, 2008.
    • (2008)
    • Madiman, M.1
  • 16
    • 84860893457 scopus 로고    scopus 로고
    • Determinant and trace inequalities for sums of positive-definite matrices, Preprint
    • M. Madiman, Determinant and trace inequalities for sums of positive-definite matrices, Preprint.
    • Madiman, M.1
  • 17
    • 34447344072 scopus 로고    scopus 로고
    • Generalized entropy power inequalities and monotonicity properties of information
    • M. Madiman, A. Barron, Generalized entropy power inequalities and monotonicity properties of information, IEEE Trans Inform Theory 53 (2007), 2317-2329.
    • (2007) IEEE Trans Inform Theory , vol.53 , pp. 2317-2329
    • Madiman, M.1    Barron, A.2
  • 18
    • 77954833632 scopus 로고    scopus 로고
    • Information-theoretic inequalities in additive combinatorics, Proc IEEE Inform Theory Workshop, Cairo, Egypt, January
    • M. Madiman, A. Marcus, P. Tetali, Information-theoretic inequalities in additive combinatorics, Proc IEEE Inform Theory Workshop, Cairo, Egypt, January 2010.
    • (2010)
    • Madiman, M.1    Marcus, A.2    Tetali, P.3
  • 19
    • 51649086113 scopus 로고    scopus 로고
    • Sandwich bounds for joint entropy, Proceedings of the IEEE International Symposium on Information Theory, Nice, June
    • M. Madiman, P. Tetali, Sandwich bounds for joint entropy, Proceedings of the IEEE International Symposium on Information Theory, Nice, June 2007.
    • (2007)
    • Madiman, M.1    Tetali, P.2
  • 20
    • 77955677572 scopus 로고    scopus 로고
    • The entropies of the sum and the difference of two IID random variables are not too different, Proc. IEEE Intl. Symp. Inform. Theory, Austin, TX, June
    • M. Madiman, I. Kontoyiannis, The entropies of the sum and the difference of two IID random variables are not too different, Proc. IEEE Intl. Symp. Inform. Theory, Austin, TX, June 2010.
    • (2010)
    • Madiman, M.1    Kontoyiannis, I.2
  • 21
    • 77957602848 scopus 로고    scopus 로고
    • Information inequalities for joint distributions, with interpretations and applications
    • M. Madiman, P. Tetali, Information inequalities for joint distributions, with interpretations and applications, IEEE Trans Inform Theory 56 (2010), 2699-2713.
    • (2010) IEEE Trans Inform Theory , vol.56 , pp. 2699-2713
    • Madiman, M.1    Tetali, P.2
  • 22
    • 33846088151 scopus 로고    scopus 로고
    • Two constructions on limits of entropy functions
    • F. Matús, Two constructions on limits of entropy functions, IEEE Trans Inform Theory 53 (2007), 320-330.
    • (2007) IEEE Trans Inform Theory , vol.53 , pp. 320-330
    • Matús, F.1
  • 23
    • 0003343714 scopus 로고    scopus 로고
    • Additive number theory: inverse problems and geometry of sumsets
    • Springer
    • M. Nathanson, Additive number theory: inverse problems and geometry of sumsets, ser. Graduate Texts in Mathematics, Vol. 165, Springer, 1996.
    • (1996) ser. Graduate Texts in Mathematics , vol.165
    • Nathanson, M.1
  • 25
    • 0013479974 scopus 로고
    • Eine zahlentheoretische Anwendung der Graphentheorie
    • H. Plünnecke, Eine zahlentheoretische Anwendung der Graphentheorie, J Reine Angew Math 243 (1970), 171-183.
    • (1970) J Reine Angew Math , vol.243 , pp. 171-183
    • Plünnecke, H.1
  • 27
    • 0013481579 scopus 로고
    • An application of graph theory to additive number theory
    • I. Z. Ruzsa, An application of graph theory to additive number theory, Scientia Ser A Math Sci (N.S.) 3 (1989), 97-109.
    • (1989) Scientia Ser A Math Sci (N.S.) , vol.3 , pp. 97-109
    • Ruzsa, I.Z.1
  • 28
    • 0043149640 scopus 로고
    • Addendum to: An application of graph theory to additive number theory
    • I. Z. Ruzsa, Addendum to: An application of graph theory to additive number theory, Scientia Ser A Math Sci (N.S.) 4 (1990/91), 93-94.
    • (1990) Scientia Ser A Math Sci (N.S.) , vol.4 , pp. 93-94
    • Ruzsa, I.Z.1
  • 29
    • 77954826479 scopus 로고    scopus 로고
    • Cardinality questions about sumsets, in Additive combinatorics, ser. CRM, Proc. Lecture Notes, Amer. Math. Soc.,Providence, RI
    • I. Z. Ruzsa, Cardinality questions about sumsets, in Additive combinatorics, ser. CRM, Proc. Lecture Notes, Amer. Math. Soc., Vol. 43, Providence, RI, 2007, pp. 195-205.
    • (2007) , vol.43 , pp. 195-205
    • Ruzsa, I.Z.1
  • 32
    • 77955775031 scopus 로고    scopus 로고
    • Sumset and inverse sumset theory for Shannon entropy
    • T. Tao, Sumset and inverse sumset theory for Shannon entropy, Comb Probab Comput 19 (2010), 603-639.
    • (2010) Comb Probab Comput , vol.19 , pp. 603-639
    • Tao, T.1
  • 34
    • 33845302486 scopus 로고    scopus 로고
    • Cambridge Studies in Advanced Mathematics 105, CUP
    • T. Tao, V. Vu, Additive Combinatorics, Cambridge Studies in Advanced Mathematics 105, CUP, 2006.
    • (2006) Additive Combinatorics
    • Tao, T.1    Vu, V.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.