메뉴 건너뛰기




Volumn 37, Issue 4, 2010, Pages 525-539

A sharp inverse Littlewood-Offord theorem

Author keywords

Additive combinatorics; Concentration probability; Inverse theorems; Littlewood offord problem; Random walks

Indexed keywords


EID: 77958533141     PISSN: 10429832     EISSN: 10982418     Source Type: Journal    
DOI: 10.1002/rsa.20327     Document Type: Article
Times cited : (45)

References (21)
  • 1
    • 0010981220 scopus 로고
    • On a lemma of Littlewood and Offord
    • P. Erdo{double acute}s, On a lemma of Littlewood and Offord, Bull Am Math Soc 51 (1945), 898-902.
    • (1945) Bull Am Math Soc , vol.51 , pp. 898-902
    • Erdos, P.1
  • 2
    • 0348042710 scopus 로고
    • Elementary problems and solutions: Solutions: E736
    • and,
    • P. Erdos, and L. Moser, Elementary problems and solutions: Solutions: E736., Am Math Mon 54 (1947), 229-230.
    • (1947) Am Math Mon , vol.54 , pp. 229-230
    • Erdos, P.1    Moser, L.2
  • 3
    • 0037663571 scopus 로고
    • Solution of the Littlewood-Offord problem in high dimensions
    • and,
    • P. Frankl, and Z. Füredi, Solution of the Littlewood-Offord problem in high dimensions, Ann Math 128 (1988), 259-270.
    • (1988) Ann Math , vol.128 , pp. 259-270
    • Frankl, P.1    Füredi, Z.2
  • 4
  • 5
    • 33645673056 scopus 로고
    • Estimates for the concentration function of combinatorial number theory and probability
    • G. Halász, Estimates for the concentration function of combinatorial number theory and probability, Period Math Hung 8 (1977), 197-211.
    • (1977) Period Math Hung , vol.8 , pp. 197-211
    • Halász, G.1
  • 6
    • 84968494236 scopus 로고
    • On the probability that a random ± 1 matrix is singular
    • and,
    • J. Kahn, J. Komlós, and E. Szemerédi, On the probability that a random ± 1 matrix is singular, J Amer Math Soc 8 (1995), 223-240.
    • (1995) J Amer Math Soc , vol.8 , pp. 223-240
    • Kahn, J.1    Komlós, J.2    Szemerédi, E.3
  • 7
    • 0038339284 scopus 로고
    • On a conjecture of Erdo{double acute}s and a stronger form of Sperner's theorem
    • G. Katona, On a conjecture of Erdo{double acute}s and a stronger form of Sperner's theorem, Stud Sci Math Hung 1 (1966), 59-63.
    • (1966) Stud Sci Math Hung , vol.1 , pp. 59-63
    • Katona, G.1
  • 8
    • 0038339282 scopus 로고
    • On a lemma of Littlewood and Offord on the distributions of linear combinations of vectors
    • D. Kleitman, On a lemma of Littlewood and Offord on the distributions of linear combinations of vectors, Adv Math 5 (1970), 155-157.
    • (1970) Adv Math , vol.5 , pp. 155-157
    • Kleitman, D.1
  • 9
    • 0030704754 scopus 로고    scopus 로고
    • Optimal representations by sumsets and subset sums
    • V. Lev, Optimal representations by sumsets and subset sums, J Num Theory 62 (1997), 127-143.
    • (1997) J Num Theory , vol.62 , pp. 127-143
    • Lev, V.1
  • 10
    • 0005272276 scopus 로고
    • On the number of real roots of a random algebraic equation. III
    • and,
    • J. E. Littlewood, and A. C. Offord, On the number of real roots of a random algebraic equation. III, Rec Math [Mat Sbornik] N S 12 (1943), 277-286.
    • (1943) Rec Math [Mat Sbornik] N S , vol.12 , pp. 277-286
    • Littlewood, J.E.1    Offord, A.C.2
  • 11
    • 41049114969 scopus 로고    scopus 로고
    • The Littlewood-Offord problem and the condition number of random matrices
    • and,
    • M. Rudelson, and R. Vershynin, The Littlewood-Offord problem and the condition number of random matrices, Adv Math 218 (2008), 600-633.
    • (2008) Adv Math , vol.218 , pp. 600-633
    • Rudelson, M.1    Vershynin, R.2
  • 12
    • 0010989222 scopus 로고
    • Finite addition theorems I
    • A. Sárko{double acute}zy, Finite addition theorems I, J Num Thy 32 (1989), 114-130.
    • (1989) J Num Thy , vol.32 , pp. 114-130
    • Sárkozy, A.1
  • 13
    • 26744445544 scopus 로고
    • Über ein Problem von Erdo{double acute}s und Moser
    • and,
    • A. Sárko{double acute}zy, and E. Szemerédi, Über ein Problem von Erdo{double acute}s und Moser, Acta Arithmetica 11 (1965), 205-208.
    • (1965) Acta Arithmetica , vol.11 , pp. 205-208
    • Sárkozy, A.1    Szemerédi, E.2
  • 14
    • 0000946102 scopus 로고
    • Weyl groups, the hard Lefschetz theorem, and the Sperner property
    • R. Stanley, Weyl groups, the hard Lefschetz theorem, and the Sperner property, SIAM J. Algebraic Discrete Methods 1 (1980), 168-184.
    • (1980) SIAM J. Algebraic Discrete Methods , vol.1 , pp. 168-184
    • Stanley, R.1
  • 15
    • 30644457842 scopus 로고    scopus 로고
    • Long arithmetic progressions in sumsets: thresholds and bounds
    • and,
    • E. Szemerédi, and V. Vu, Long arithmetic progressions in sumsets: thresholds and bounds, J Amer Math Soc 19 (2006), 119-169.
    • (2006) J Amer Math Soc , vol.19 , pp. 119-169
    • Szemerédi, E.1    Vu, V.2
  • 16
    • 33645288547 scopus 로고    scopus 로고
    • On random (-1, 1) matrices: Singularity and determinant
    • and,
    • T. Tao, and V. Vu, On random (-1, 1) matrices: Singularity and determinant, Random Struct Algorithms 28 (2006), 1-23.
    • (2006) Random Struct Algorithms , vol.28 , pp. 1-23
    • Tao, T.1    Vu, V.2
  • 17
    • 41049103477 scopus 로고    scopus 로고
    • On the singularity probability of random Bernoulli matrices
    • and,
    • T. Tao, and V. Vu, On the singularity probability of random Bernoulli matrices, J A. M. S 20 (2007), 603-673.
    • (2007) J A. M. S , vol.20 , pp. 603-673
    • Tao, T.1    Vu, V.2
  • 18
    • 48949102370 scopus 로고    scopus 로고
    • John type theorems for generalized arithmetic progressions and iterated sumsets
    • and,
    • T. Tao, and V. Vu, John type theorems for generalized arithmetic progressions and iterated sumsets, Adv Math 219 (2008), 428-449.
    • (2008) Adv Math , vol.219 , pp. 428-449
    • Tao, T.1    Vu, V.2
  • 19
    • 71849089047 scopus 로고    scopus 로고
    • Inverse Littlewood-Offord theorems and the condition number of random matrices
    • and,
    • T. Tao, and V. Vu, Inverse Littlewood-Offord theorems and the condition number of random matrices, Ann Math 169 (2009), 595-632.
    • (2009) Ann Math , vol.169 , pp. 595-632
    • Tao, T.1    Vu, V.2
  • 20
    • 44249125025 scopus 로고    scopus 로고
    • Random matrices: The circular law
    • and,
    • T. Tao, and V. Vu, Random matrices: The circular law, Commun Contemp Math 10 (2008), 261-307.
    • (2008) Commun Contemp Math , vol.10 , pp. 261-307
    • Tao, T.1    Vu, V.2
  • 21
    • 33845302486 scopus 로고    scopus 로고
    • Additive combinatorics
    • and, Cambridge University Press, Cambridge, UK,
    • T. Tao, and V. Vu, Additive combinatorics, Cambridge University Press, Cambridge, UK, 2006.
    • (2006)
    • Tao, T.1    Vu, V.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.