1/3–2/3 conjecture (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "1/3–2/3 conjecture" in English language version.

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19doi.org

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16semanticscholar.org

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6ams.org

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3psu.edu

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3arxiv.org

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1springer.com

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ams.org

mathscinet.ams.org

Kahn & Saks (1984); Brightwell, Felsner & Trotter (1995). Kahn, Jeff; Saks, Michael (1984), "Balancing poset extensions", Order, 1 (2): 113–126, doi:10.1007/BF00565647, S2CID 123370506. Brightwell, Graham R.; Felsner, Stefan; Trotter, William T. (1995), "Balancing pairs and the cross product conjecture", Order, 12 (4): 327–349, CiteSeerX 10.1.1.38.7841, doi:10.1007/BF01110378, MR 1368815, S2CID 14793475.
Brightwell, Felsner & Trotter (1995). Brightwell, Graham R.; Felsner, Stefan; Trotter, William T. (1995), "Balancing pairs and the cross product conjecture", Order, 12 (4): 327–349, CiteSeerX 10.1.1.38.7841, doi:10.1007/BF01110378, MR 1368815, S2CID 14793475.
Linial (1984), Theorem 2; Sah (2021). Linial, Nati (1984), "The information-theoretic bound is good for merging", SIAM Journal on Computing, 13 (4): 795–801, doi:10.1137/0213049, S2CID 5149351. Sah, Ashwin (2021), "Improving the ${\tfrac {1}{3}}$ – ${\tfrac {2}{3}}$ conjecture for width two posets", Combinatorica, 41 (1): 99–126, arXiv:1811.01500, doi:10.1007/s00493-020-4091-3, MR 4235316, S2CID 119604901
Zaguia (2019). Zaguia, Imed (2019), "The 1/3–2/3 conjecture for ordered sets whose cover graph is a forest", Order, 36 (2): 335–347, arXiv:1610.00809, doi:10.1007/s11083-018-9469-0, MR 3983482, S2CID 119631612.
Brightwell, Felsner & Trotter (1995); Kahn & Saks (1984); Khachiyan (1989); Kahn & Linial (1991); Felsner & Trotter (1993). Brightwell, Graham R.; Felsner, Stefan; Trotter, William T. (1995), "Balancing pairs and the cross product conjecture", Order, 12 (4): 327–349, CiteSeerX 10.1.1.38.7841, doi:10.1007/BF01110378, MR 1368815, S2CID 14793475. Kahn, Jeff; Saks, Michael (1984), "Balancing poset extensions", Order, 1 (2): 113–126, doi:10.1007/BF00565647, S2CID 123370506. Khachiyan, Leonid (1989), "Optimal algorithms in convex programming decomposition and sorting", in Jaravlev, J. (ed.), Computers and Decision Problems (in Russian), Moscow: Nauka, pp. 161–205. As cited by Brightwell, Felsner & Trotter (1995). Kahn, Jeff; Linial, Nati (1991), "Balancing extensions via Brunn-Minkowski", Combinatorica, 11 (4): 363–368, doi:10.1007/BF01275670, S2CID 206793172. Felsner, Stefan; Trotter, William T. (1993), "Balancing pairs in partially ordered sets", Combinatorics, Paul Erdős is eighty, Bolyai Society Mathematical Studies, vol. 1, Budapest: János Bolyai Mathematical Society, pp. 145–157, MR 1249709.
Peczarski (2019). Peczarski, Marcin (2019), "The worst balanced partially ordered sets—ladders with broken rungs", Experimental Mathematics, 28 (2): 181–184, doi:10.1080/10586458.2017.1368050, MR 3955809, S2CID 125593629.

arxiv.org

Linial (1984), Theorem 2; Sah (2021). Linial, Nati (1984), "The information-theoretic bound is good for merging", SIAM Journal on Computing, 13 (4): 795–801, doi:10.1137/0213049, S2CID 5149351. Sah, Ashwin (2021), "Improving the ${\tfrac {1}{3}}$ – ${\tfrac {2}{3}}$ conjecture for width two posets", Combinatorica, 41 (1): 99–126, arXiv:1811.01500, doi:10.1007/s00493-020-4091-3, MR 4235316, S2CID 119604901
Zaguia (2012). Zaguia, Imed (2012), "The 1/3-2/3 Conjecture for N-free ordered sets", Electronic Journal of Combinatorics, 19 (2): P29, arXiv:1107.5626, doi:10.37236/2345, S2CID 1979845.
Zaguia (2019). Zaguia, Imed (2019), "The 1/3–2/3 conjecture for ordered sets whose cover graph is a forest", Order, 36 (2): 335–347, arXiv:1610.00809, doi:10.1007/s11083-018-9469-0, MR 3983482, S2CID 119631612.

doi.org

Kahn & Saks (1984); Brightwell, Felsner & Trotter (1995). Kahn, Jeff; Saks, Michael (1984), "Balancing poset extensions", Order, 1 (2): 113–126, doi:10.1007/BF00565647, S2CID 123370506. Brightwell, Graham R.; Felsner, Stefan; Trotter, William T. (1995), "Balancing pairs and the cross product conjecture", Order, 12 (4): 327–349, CiteSeerX 10.1.1.38.7841, doi:10.1007/BF01110378, MR 1368815, S2CID 14793475.
Brightwell, Felsner & Trotter (1995). Brightwell, Graham R.; Felsner, Stefan; Trotter, William T. (1995), "Balancing pairs and the cross product conjecture", Order, 12 (4): 327–349, CiteSeerX 10.1.1.38.7841, doi:10.1007/BF01110378, MR 1368815, S2CID 14793475.
Kahn & Saks (1984) Kahn, Jeff; Saks, Michael (1984), "Balancing poset extensions", Order, 1 (2): 113–126, doi:10.1007/BF00565647, S2CID 123370506.
Kislitsyn (1968) Kislitsyn, S. S. (1968), "A finite partially ordered set and its corresponding set of permutations", Mathematical Notes, 4 (5): 798–801, doi:10.1007/BF01111312, S2CID 120228193.
However, despite the close connection of Fredman (1976) to the problem of sorting partially ordered data and hence to the 1/3–2/3 conjecture, it is not mentioned in that paper. Fredman, M. L. (1976), "How good is the information theory bound in sorting?", Theoretical Computer Science, 1 (4): 355–361, doi:10.1016/0304-3975(76)90078-5
Brightwell (1999) Brightwell, Graham R. (1999), "Balanced pairs in partial orders", Discrete Mathematics, 201 (1–3): 25–52, doi:10.1016/S0012-365X(98)00311-2.
Linial (1984), Theorem 2; Sah (2021). Linial, Nati (1984), "The information-theoretic bound is good for merging", SIAM Journal on Computing, 13 (4): 795–801, doi:10.1137/0213049, S2CID 5149351. Sah, Ashwin (2021), "Improving the ${\tfrac {1}{3}}$ – ${\tfrac {2}{3}}$ conjecture for width two posets", Combinatorica, 41 (1): 99–126, arXiv:1811.01500, doi:10.1007/s00493-020-4091-3, MR 4235316, S2CID 119604901
Trotter, Gehrlein & Fishburn (1992). Trotter, William T.; Gehrlein, William V.; Fishburn, Peter C. (1992), "Balance theorems for height-2 posets", Order, 9 (1): 43–53, doi:10.1007/BF00419038, S2CID 16157076.
Peczarski (2006). Peczarski, Marcin (2006), "The gold partition conjecture", Order, 23 (1): 89–95, doi:10.1007/s11083-006-9033-1, S2CID 42415160.
Peczarski (2008). Peczarski, Marcin (2008), "The gold partition conjecture for 6-thin posets", Order, 25 (2): 91–103, doi:10.1007/s11083-008-9081-9, S2CID 42034095.
Zaguia (2012). Zaguia, Imed (2012), "The 1/3-2/3 Conjecture for N-free ordered sets", Electronic Journal of Combinatorics, 19 (2): P29, arXiv:1107.5626, doi:10.37236/2345, S2CID 1979845.
Brightwell (1989). Brightwell, Graham R. (1989), "Semiorders and the 1/3–2/3 conjecture", Order, 5 (4): 369–380, doi:10.1007/BF00353656, S2CID 86860160.
Zaguia (2019). Zaguia, Imed (2019), "The 1/3–2/3 conjecture for ordered sets whose cover graph is a forest", Order, 36 (2): 335–347, arXiv:1610.00809, doi:10.1007/s11083-018-9469-0, MR 3983482, S2CID 119631612.
Brightwell, Felsner & Trotter (1995); Kahn & Saks (1984); Khachiyan (1989); Kahn & Linial (1991); Felsner & Trotter (1993). Brightwell, Graham R.; Felsner, Stefan; Trotter, William T. (1995), "Balancing pairs and the cross product conjecture", Order, 12 (4): 327–349, CiteSeerX 10.1.1.38.7841, doi:10.1007/BF01110378, MR 1368815, S2CID 14793475. Kahn, Jeff; Saks, Michael (1984), "Balancing poset extensions", Order, 1 (2): 113–126, doi:10.1007/BF00565647, S2CID 123370506. Khachiyan, Leonid (1989), "Optimal algorithms in convex programming decomposition and sorting", in Jaravlev, J. (ed.), Computers and Decision Problems (in Russian), Moscow: Nauka, pp. 161–205. As cited by Brightwell, Felsner & Trotter (1995). Kahn, Jeff; Linial, Nati (1991), "Balancing extensions via Brunn-Minkowski", Combinatorica, 11 (4): 363–368, doi:10.1007/BF01275670, S2CID 206793172. Felsner, Stefan; Trotter, William T. (1993), "Balancing pairs in partially ordered sets", Combinatorics, Paul Erdős is eighty, Bolyai Society Mathematical Studies, vol. 1, Budapest: János Bolyai Mathematical Society, pp. 145–157, MR 1249709.
Fredman (1976) Fredman, M. L. (1976), "How good is the information theory bound in sorting?", Theoretical Computer Science, 1 (4): 355–361, doi:10.1016/0304-3975(76)90078-5
Kahn & Saks (1984). Kahn, Jeff; Saks, Michael (1984), "Balancing poset extensions", Order, 1 (2): 113–126, doi:10.1007/BF00565647, S2CID 123370506.
Saks (1985). Saks, Michael (1985), "Balancing linear extensions of ordered sets", Unsolved problems, Order, 2: 327–330, doi:10.1007/BF00333138, S2CID 189901558
Peczarski (2019). Peczarski, Marcin (2019), "The worst balanced partially ordered sets—ladders with broken rungs", Experimental Mathematics, 28 (2): 181–184, doi:10.1080/10586458.2017.1368050, MR 3955809, S2CID 125593629.
Brightwell & Winkler (1991). Brightwell, Graham R.; Winkler, Peter (1991), "Counting linear extensions", Order, 8 (3): 225–242, doi:10.1007/BF00383444, S2CID 119697949.

psu.edu

citeseerx.ist.psu.edu

Kahn & Saks (1984); Brightwell, Felsner & Trotter (1995). Kahn, Jeff; Saks, Michael (1984), "Balancing poset extensions", Order, 1 (2): 113–126, doi:10.1007/BF00565647, S2CID 123370506. Brightwell, Graham R.; Felsner, Stefan; Trotter, William T. (1995), "Balancing pairs and the cross product conjecture", Order, 12 (4): 327–349, CiteSeerX 10.1.1.38.7841, doi:10.1007/BF01110378, MR 1368815, S2CID 14793475.
Brightwell, Felsner & Trotter (1995). Brightwell, Graham R.; Felsner, Stefan; Trotter, William T. (1995), "Balancing pairs and the cross product conjecture", Order, 12 (4): 327–349, CiteSeerX 10.1.1.38.7841, doi:10.1007/BF01110378, MR 1368815, S2CID 14793475.
Brightwell, Felsner & Trotter (1995); Kahn & Saks (1984); Khachiyan (1989); Kahn & Linial (1991); Felsner & Trotter (1993). Brightwell, Graham R.; Felsner, Stefan; Trotter, William T. (1995), "Balancing pairs and the cross product conjecture", Order, 12 (4): 327–349, CiteSeerX 10.1.1.38.7841, doi:10.1007/BF01110378, MR 1368815, S2CID 14793475. Kahn, Jeff; Saks, Michael (1984), "Balancing poset extensions", Order, 1 (2): 113–126, doi:10.1007/BF00565647, S2CID 123370506. Khachiyan, Leonid (1989), "Optimal algorithms in convex programming decomposition and sorting", in Jaravlev, J. (ed.), Computers and Decision Problems (in Russian), Moscow: Nauka, pp. 161–205. As cited by Brightwell, Felsner & Trotter (1995). Kahn, Jeff; Linial, Nati (1991), "Balancing extensions via Brunn-Minkowski", Combinatorica, 11 (4): 363–368, doi:10.1007/BF01275670, S2CID 206793172. Felsner, Stefan; Trotter, William T. (1993), "Balancing pairs in partially ordered sets", Combinatorics, Paul Erdős is eighty, Bolyai Society Mathematical Studies, vol. 1, Budapest: János Bolyai Mathematical Society, pp. 145–157, MR 1249709.

semanticscholar.org

api.semanticscholar.org

Kahn & Saks (1984); Brightwell, Felsner & Trotter (1995). Kahn, Jeff; Saks, Michael (1984), "Balancing poset extensions", Order, 1 (2): 113–126, doi:10.1007/BF00565647, S2CID 123370506. Brightwell, Graham R.; Felsner, Stefan; Trotter, William T. (1995), "Balancing pairs and the cross product conjecture", Order, 12 (4): 327–349, CiteSeerX 10.1.1.38.7841, doi:10.1007/BF01110378, MR 1368815, S2CID 14793475.
Brightwell, Felsner & Trotter (1995). Brightwell, Graham R.; Felsner, Stefan; Trotter, William T. (1995), "Balancing pairs and the cross product conjecture", Order, 12 (4): 327–349, CiteSeerX 10.1.1.38.7841, doi:10.1007/BF01110378, MR 1368815, S2CID 14793475.
Kahn & Saks (1984) Kahn, Jeff; Saks, Michael (1984), "Balancing poset extensions", Order, 1 (2): 113–126, doi:10.1007/BF00565647, S2CID 123370506.
Kislitsyn (1968) Kislitsyn, S. S. (1968), "A finite partially ordered set and its corresponding set of permutations", Mathematical Notes, 4 (5): 798–801, doi:10.1007/BF01111312, S2CID 120228193.
Linial (1984), Theorem 2; Sah (2021). Linial, Nati (1984), "The information-theoretic bound is good for merging", SIAM Journal on Computing, 13 (4): 795–801, doi:10.1137/0213049, S2CID 5149351. Sah, Ashwin (2021), "Improving the ${\tfrac {1}{3}}$ – ${\tfrac {2}{3}}$ conjecture for width two posets", Combinatorica, 41 (1): 99–126, arXiv:1811.01500, doi:10.1007/s00493-020-4091-3, MR 4235316, S2CID 119604901
Trotter, Gehrlein & Fishburn (1992). Trotter, William T.; Gehrlein, William V.; Fishburn, Peter C. (1992), "Balance theorems for height-2 posets", Order, 9 (1): 43–53, doi:10.1007/BF00419038, S2CID 16157076.
Peczarski (2006). Peczarski, Marcin (2006), "The gold partition conjecture", Order, 23 (1): 89–95, doi:10.1007/s11083-006-9033-1, S2CID 42415160.
Peczarski (2008). Peczarski, Marcin (2008), "The gold partition conjecture for 6-thin posets", Order, 25 (2): 91–103, doi:10.1007/s11083-008-9081-9, S2CID 42034095.
Zaguia (2012). Zaguia, Imed (2012), "The 1/3-2/3 Conjecture for N-free ordered sets", Electronic Journal of Combinatorics, 19 (2): P29, arXiv:1107.5626, doi:10.37236/2345, S2CID 1979845.
Brightwell (1989). Brightwell, Graham R. (1989), "Semiorders and the 1/3–2/3 conjecture", Order, 5 (4): 369–380, doi:10.1007/BF00353656, S2CID 86860160.
Zaguia (2019). Zaguia, Imed (2019), "The 1/3–2/3 conjecture for ordered sets whose cover graph is a forest", Order, 36 (2): 335–347, arXiv:1610.00809, doi:10.1007/s11083-018-9469-0, MR 3983482, S2CID 119631612.
Brightwell, Felsner & Trotter (1995); Kahn & Saks (1984); Khachiyan (1989); Kahn & Linial (1991); Felsner & Trotter (1993). Brightwell, Graham R.; Felsner, Stefan; Trotter, William T. (1995), "Balancing pairs and the cross product conjecture", Order, 12 (4): 327–349, CiteSeerX 10.1.1.38.7841, doi:10.1007/BF01110378, MR 1368815, S2CID 14793475. Kahn, Jeff; Saks, Michael (1984), "Balancing poset extensions", Order, 1 (2): 113–126, doi:10.1007/BF00565647, S2CID 123370506. Khachiyan, Leonid (1989), "Optimal algorithms in convex programming decomposition and sorting", in Jaravlev, J. (ed.), Computers and Decision Problems (in Russian), Moscow: Nauka, pp. 161–205. As cited by Brightwell, Felsner & Trotter (1995). Kahn, Jeff; Linial, Nati (1991), "Balancing extensions via Brunn-Minkowski", Combinatorica, 11 (4): 363–368, doi:10.1007/BF01275670, S2CID 206793172. Felsner, Stefan; Trotter, William T. (1993), "Balancing pairs in partially ordered sets", Combinatorics, Paul Erdős is eighty, Bolyai Society Mathematical Studies, vol. 1, Budapest: János Bolyai Mathematical Society, pp. 145–157, MR 1249709.
Kahn & Saks (1984). Kahn, Jeff; Saks, Michael (1984), "Balancing poset extensions", Order, 1 (2): 113–126, doi:10.1007/BF00565647, S2CID 123370506.
Saks (1985). Saks, Michael (1985), "Balancing linear extensions of ordered sets", Unsolved problems, Order, 2: 327–330, doi:10.1007/BF00333138, S2CID 189901558
Peczarski (2019). Peczarski, Marcin (2019), "The worst balanced partially ordered sets—ladders with broken rungs", Experimental Mathematics, 28 (2): 181–184, doi:10.1080/10586458.2017.1368050, MR 3955809, S2CID 125593629.
Brightwell & Winkler (1991). Brightwell, Graham R.; Winkler, Peter (1991), "Counting linear extensions", Order, 8 (3): 225–242, doi:10.1007/BF00383444, S2CID 119697949.

springer.com

link.springer.com

Saks (1985). Saks, Michael (1985), "Balancing linear extensions of ordered sets", Unsolved problems, Order, 2: 327–330, doi:10.1007/BF00333138, S2CID 189901558