Sperner's lemma (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Sperner's lemma" in English language version.

Last modified: 21:20:49, 4 September 2026 (UTC)

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2019doi.org

2^nd place

119arxiv.org

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109semanticscholar.org

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98worldcat.org

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76ams.org

434^th place

249^th place

44jstor.org

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33claremont.edu

low place

6,768^th place

22sciencedirect.com

137^th place

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21siam.org

9,070^th place

5,832^nd place

22nih.gov

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11mathpages.blogspot.com

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11ru.nl

7,619^th place

6,271^st place

11adsabs.harvard.edu

14^th place

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adsabs.harvard.edu (Global: 14^th place; English: 9^th place)

ui.adsabs.harvard.edu

Brown, A. B.; Cairns, S. S. (1961-01-01). "Strengthening of Sperner's Lemma Applied to Homology Theory". Proceedings of the National Academy of Sciences. 47 (1): 113–114. Bibcode:1961PNAS...47..113B. doi:10.1073/pnas.47.1.113. ISSN 0027-8424. PMC 285253. PMID 16590803.

ams.org (Global: 434^th place; English: 249^th place)

mathscinet.ams.org

Atanassov, K. T. (1996), "On Sperner's lemma", Studia Scientiarum Mathematicarum Hungarica, 32 (1–2): 71–74, MR 1405126
De Loera, Jesus A.; Peterson, Elisha; Su, Francis Edward (2002), "A polytopal generalization of Sperner's lemma", Journal of Combinatorial Theory, Series A, 100 (1): 1–26, doi:10.1006/jcta.2002.3274, MR 1932067
Musin, Oleg R. (2015), "Sperner type lemma for quadrangulations", Moscow Journal of Combinatorics and Number Theory, 5 (1–2): 26–35, arXiv:1406.5082, MR 3476207
Niedermaier, Andrew; Rizzolo, Douglas; Su, Francis Edward (2014), "A tree Sperner lemma", in Barg, Alexander; Musin, Oleg R. (eds.), Discrete Geometry and Algebraic Combinatorics, Contemporary Mathematics, vol. 625, Providence, RI: American Mathematical Society, pp. 77–92, arXiv:0909.0339, doi:10.1090/conm/625/12492, ISBN 9781470409050, MR 3289406, S2CID 115157240
Sperner, Emanuel (1980), "Fifty years of further development of a combinatorial lemma", Numerical solution of highly nonlinear problems (Sympos. Fixed Point Algorithms and Complementarity Problems, Univ. Southampton, Southampton, 1979), North-Holland, Amsterdam-New York, pp. 183–197, 199–217, MR 0559121
Nyman, Kathryn L.; Su, Francis Edward (2013), "A Borsuk–Ulam equivalent that directly implies Sperner's lemma", The American Mathematical Monthly, 120 (4): 346–354, doi:10.4169/amer.math.monthly.120.04.346, JSTOR 10.4169/amer.math.monthly.120.04.346, MR 3035127

arxiv.org (Global: 49^th place; English: 31^st place)

Musin, Oleg R. (2015-05-01). "Extensions of Sperner and Tucker's lemma for manifolds". Journal of Combinatorial Theory. Series A. 132: 172–187. arXiv:1212.1899. doi:10.1016/j.jcta.2014.12.001. ISSN 0097-3165. S2CID 5699192.
Asada, Megumi; Frick, Florian; Pisharody, Vivek; Polevy, Maxwell; Stoner, David; Tsang, Ling Hei; Wellner, Zoe (2018-01-01). "Fair Division and Generalizations of Sperner- and KKM-type Results". SIAM Journal on Discrete Mathematics. 32 (1): 591–610. arXiv:1701.04955. doi:10.1137/17M1116210. ISSN 0895-4801. S2CID 43932757.
Musin, Oleg R. (2015), "Sperner type lemma for quadrangulations", Moscow Journal of Combinatorics and Number Theory, 5 (1–2): 26–35, arXiv:1406.5082, MR 3476207
Meunier, Frédéric; Su, Francis Edward (2019). "Multilabeled versions of Sperner's and Fan's lemmas and applications". SIAM Journal on Applied Algebra and Geometry. 3 (3): 391–411. arXiv:1801.02044. doi:10.1137/18M1192548. S2CID 3762597.
Asada, Megumi; Frick, Florian; Pisharody, Vivek; Polevy, Maxwell; Stoner, David; Tsang, Ling Hei; Wellner, Zoe (2018). "SIAM (Society for Industrial and Applied Mathematics)". SIAM Journal on Discrete Mathematics. 32: 591–610. arXiv:1701.04955. doi:10.1137/17m1116210. S2CID 43932757.
Oleg R Musin (2014). "Around Sperner's lemma". arXiv:1405.7513 [math.CO].
Niedermaier, Andrew; Rizzolo, Douglas; Su, Francis Edward (2014), "A tree Sperner lemma", in Barg, Alexander; Musin, Oleg R. (eds.), Discrete Geometry and Algebraic Combinatorics, Contemporary Mathematics, vol. 625, Providence, RI: American Mathematical Society, pp. 77–92, arXiv:0909.0339, doi:10.1090/conm/625/12492, ISBN 9781470409050, MR 3289406, S2CID 115157240
Mirzakhani, Maryam; Vondrák, Jan (2017), "Sperner's Colorings and Optimal Partitioning of the Simplex", in Loebl, Martin; Nešetřil, Jaroslav; Thomas, Robin (eds.), A Journey Through Discrete Mathematics: A Tribute to Jiří Matoušek, Cham: Springer International Publishing, pp. 615–631, arXiv:1611.08339, doi:10.1007/978-3-319-44479-6_25, ISBN 978-3-319-44479-6, S2CID 38668858, retrieved 2022-04-25
Gidea, Marian; Shmalo, Yitzchak (2018). "Combinatorial approach to detection of fixed points, periodic orbits, and symbolic dynamics". Discrete & Continuous Dynamical Systems - A. 38 (12). American Institute of Mathematical Sciences (AIMS): 6123–6148. arXiv:1706.08960. doi:10.3934/dcds.2018264. ISSN 1553-5231. S2CID 119130905.

claremont.edu (Global: low place; English: 6,768^th place)

scholarship.claremont.edu

De Loera, Jesus A.; Peterson, Elisha; Su, Francis Edward (2002), "A polytopal generalization of Sperner's lemma", Journal of Combinatorial Theory, Series A, 100 (1): 1–26, doi:10.1006/jcta.2002.3274, MR 1932067
Su, F. E. (1999). "Rental Harmony: Sperner's Lemma in Fair Division". The American Mathematical Monthly. 106 (10): 930–942. doi:10.2307/2589747. JSTOR 2589747.
Nyman, Kathryn L.; Su, Francis Edward (2013), "A Borsuk–Ulam equivalent that directly implies Sperner's lemma", The American Mathematical Monthly, 120 (4): 346–354, doi:10.4169/amer.math.monthly.120.04.346, JSTOR 10.4169/amer.math.monthly.120.04.346, MR 3035127

doi.org (Global: 2^nd place; English: 2^nd place)

McLennan, Andrew; Tourky, Rabee (2008). "Using Volume to Prove Sperner's Lemma". Economic Theory. 35 (3): 593–597. doi:10.1007/s00199-007-0257-0. ISSN 0938-2259. JSTOR 40282878.
Chen, Xi; Deng, Xiaotie (2009-10-17). "On the complexity of 2D discrete fixed point problem". Theoretical Computer Science. Automata, Languages and Programming (ICALP 2006). 410 (44): 4448–4456. doi:10.1016/j.tcs.2009.07.052. ISSN 0304-3975. S2CID 2831759.
De Loera, Jesus A.; Peterson, Elisha; Su, Francis Edward (2002), "A polytopal generalization of Sperner's lemma", Journal of Combinatorial Theory, Series A, 100 (1): 1–26, doi:10.1006/jcta.2002.3274, MR 1932067
Meunier, Frédéric (2006-10-01). "Sperner labellings: A combinatorial approach". Journal of Combinatorial Theory. Series A. 113 (7): 1462–1475. doi:10.1016/j.jcta.2006.01.006. ISSN 0097-3165.
Musin, Oleg R. (2015-05-01). "Extensions of Sperner and Tucker's lemma for manifolds". Journal of Combinatorial Theory. Series A. 132: 172–187. arXiv:1212.1899. doi:10.1016/j.jcta.2014.12.001. ISSN 0097-3165. S2CID 5699192.
Asada, Megumi; Frick, Florian; Pisharody, Vivek; Polevy, Maxwell; Stoner, David; Tsang, Ling Hei; Wellner, Zoe (2018-01-01). "Fair Division and Generalizations of Sperner- and KKM-type Results". SIAM Journal on Discrete Mathematics. 32 (1): 591–610. arXiv:1701.04955. doi:10.1137/17M1116210. ISSN 0895-4801. S2CID 43932757.
Kuhn, H. W. (1960), "Some Combinatorial Lemmas in Topology", IBM Journal of Research and Development, 4 (5): 518–524, doi:10.1147/rd.45.0518
Wolsey, Laurence A (1977-07-01). "Cubical sperner lemmas as applications of generalized complementary pivoting". Journal of Combinatorial Theory. Series A. 23 (1): 78–87. doi:10.1016/0097-3165(77)90081-4. ISSN 0097-3165.
Bapat, R. B. (1989). "A constructive proof of a permutation-based generalization of Sperner's lemma". Mathematical Programming. 44 (1–3): 113–120. doi:10.1007/BF01587081. S2CID 5325605.
Su, F. E. (1999). "Rental Harmony: Sperner's Lemma in Fair Division". The American Mathematical Monthly. 106 (10): 930–942. doi:10.2307/2589747. JSTOR 2589747.
Meunier, Frédéric; Su, Francis Edward (2019). "Multilabeled versions of Sperner's and Fan's lemmas and applications". SIAM Journal on Applied Algebra and Geometry. 3 (3): 391–411. arXiv:1801.02044. doi:10.1137/18M1192548. S2CID 3762597.
Asada, Megumi; Frick, Florian; Pisharody, Vivek; Polevy, Maxwell; Stoner, David; Tsang, Ling Hei; Wellner, Zoe (2018). "SIAM (Society for Industrial and Applied Mathematics)". SIAM Journal on Discrete Mathematics. 32: 591–610. arXiv:1701.04955. doi:10.1137/17m1116210. S2CID 43932757.
Brown, A. B.; Cairns, S. S. (1961-01-01). "Strengthening of Sperner's Lemma Applied to Homology Theory". Proceedings of the National Academy of Sciences. 47 (1): 113–114. Bibcode:1961PNAS...47..113B. doi:10.1073/pnas.47.1.113. ISSN 0027-8424. PMC 285253. PMID 16590803.
Niedermaier, Andrew; Rizzolo, Douglas; Su, Francis Edward (2014), "A tree Sperner lemma", in Barg, Alexander; Musin, Oleg R. (eds.), Discrete Geometry and Algebraic Combinatorics, Contemporary Mathematics, vol. 625, Providence, RI: American Mathematical Society, pp. 77–92, arXiv:0909.0339, doi:10.1090/conm/625/12492, ISBN 9781470409050, MR 3289406, S2CID 115157240
Mirzakhani, Maryam; Vondrák, Jan (2017), "Sperner's Colorings and Optimal Partitioning of the Simplex", in Loebl, Martin; Nešetřil, Jaroslav; Thomas, Robin (eds.), A Journey Through Discrete Mathematics: A Tribute to Jiří Matoušek, Cham: Springer International Publishing, pp. 615–631, arXiv:1611.08339, doi:10.1007/978-3-319-44479-6_25, ISBN 978-3-319-44479-6, S2CID 38668858, retrieved 2022-04-25
Gidea, Marian; Shmalo, Yitzchak (2018). "Combinatorial approach to detection of fixed points, periodic orbits, and symbolic dynamics". Discrete & Continuous Dynamical Systems - A. 38 (12). American Institute of Mathematical Sciences (AIMS): 6123–6148. arXiv:1706.08960. doi:10.3934/dcds.2018264. ISSN 1553-5231. S2CID 119130905.
Aigner, Martin; Ziegler, Günter M. (2010), "One square and an odd number of triangles", Proofs from The Book (4th ed.), Berlin: Springer-Verlag, pp. 131–138, doi:10.1007/978-3-642-00856-6_20, ISBN 978-3-642-00855-9
Scarf, Herbert (1967). "The Core of an N Person Game". Econometrica. 35 (1): 50–69. doi:10.2307/1909383. JSTOR 1909383.
Nyman, Kathryn L.; Su, Francis Edward (2013), "A Borsuk–Ulam equivalent that directly implies Sperner's lemma", The American Mathematical Monthly, 120 (4): 346–354, doi:10.4169/amer.math.monthly.120.04.346, JSTOR 10.4169/amer.math.monthly.120.04.346, MR 3035127

jstor.org (Global: 23^rd place; English: 15^th place)

McLennan, Andrew; Tourky, Rabee (2008). "Using Volume to Prove Sperner's Lemma". Economic Theory. 35 (3): 593–597. doi:10.1007/s00199-007-0257-0. ISSN 0938-2259. JSTOR 40282878.
Su, F. E. (1999). "Rental Harmony: Sperner's Lemma in Fair Division". The American Mathematical Monthly. 106 (10): 930–942. doi:10.2307/2589747. JSTOR 2589747.
Scarf, Herbert (1967). "The Core of an N Person Game". Econometrica. 35 (1): 50–69. doi:10.2307/1909383. JSTOR 1909383.
Nyman, Kathryn L.; Su, Francis Edward (2013), "A Borsuk–Ulam equivalent that directly implies Sperner's lemma", The American Mathematical Monthly, 120 (4): 346–354, doi:10.4169/amer.math.monthly.120.04.346, JSTOR 10.4169/amer.math.monthly.120.04.346, MR 3035127

mathpages.blogspot.com (Global: low place; English: low place)

Anatoly (2010-05-21). "Sperner's lemma". Math Pages Blog. Retrieved 2024-07-20.

nih.gov (Global: 5^th place; English: 5^th place)

ncbi.nlm.nih.gov

Brown, A. B.; Cairns, S. S. (1961-01-01). "Strengthening of Sperner's Lemma Applied to Homology Theory". Proceedings of the National Academy of Sciences. 47 (1): 113–114. Bibcode:1961PNAS...47..113B. doi:10.1073/pnas.47.1.113. ISSN 0027-8424. PMC 285253. PMID 16590803.

pubmed.ncbi.nlm.nih.gov

Brown, A. B.; Cairns, S. S. (1961-01-01). "Strengthening of Sperner's Lemma Applied to Homology Theory". Proceedings of the National Academy of Sciences. 47 (1): 113–114. Bibcode:1961PNAS...47..113B. doi:10.1073/pnas.47.1.113. ISSN 0027-8424. PMC 285253. PMID 16590803.

ru.nl (Global: 7,619^th place; English: 6,271^st place)

math.ru.nl

Michael Müger (2016), Topology for the working mathematician (PDF), Draft

sciencedirect.com (Global: 137^th place; English: 146^th place)

Chen, Xi; Deng, Xiaotie (2009-10-17). "On the complexity of 2D discrete fixed point problem". Theoretical Computer Science. Automata, Languages and Programming (ICALP 2006). 410 (44): 4448–4456. doi:10.1016/j.tcs.2009.07.052. ISSN 0304-3975. S2CID 2831759.
Shapley, L. S. (1973-01-01), "On Balanced Games without Side Payments", in Hu, T. C.; Robinson, Stephen M. (eds.), Mathematical Programming, Academic Press, pp. 261–290, ISBN 978-0-12-358350-5, retrieved 2020-06-29

semanticscholar.org (Global: 15^th place; English: 8^th place)

api.semanticscholar.org

Chen, Xi; Deng, Xiaotie (2009-10-17). "On the complexity of 2D discrete fixed point problem". Theoretical Computer Science. Automata, Languages and Programming (ICALP 2006). 410 (44): 4448–4456. doi:10.1016/j.tcs.2009.07.052. ISSN 0304-3975. S2CID 2831759.
Musin, Oleg R. (2015-05-01). "Extensions of Sperner and Tucker's lemma for manifolds". Journal of Combinatorial Theory. Series A. 132: 172–187. arXiv:1212.1899. doi:10.1016/j.jcta.2014.12.001. ISSN 0097-3165. S2CID 5699192.
Asada, Megumi; Frick, Florian; Pisharody, Vivek; Polevy, Maxwell; Stoner, David; Tsang, Ling Hei; Wellner, Zoe (2018-01-01). "Fair Division and Generalizations of Sperner- and KKM-type Results". SIAM Journal on Discrete Mathematics. 32 (1): 591–610. arXiv:1701.04955. doi:10.1137/17M1116210. ISSN 0895-4801. S2CID 43932757.
Bapat, R. B. (1989). "A constructive proof of a permutation-based generalization of Sperner's lemma". Mathematical Programming. 44 (1–3): 113–120. doi:10.1007/BF01587081. S2CID 5325605.
Meunier, Frédéric; Su, Francis Edward (2019). "Multilabeled versions of Sperner's and Fan's lemmas and applications". SIAM Journal on Applied Algebra and Geometry. 3 (3): 391–411. arXiv:1801.02044. doi:10.1137/18M1192548. S2CID 3762597.
Asada, Megumi; Frick, Florian; Pisharody, Vivek; Polevy, Maxwell; Stoner, David; Tsang, Ling Hei; Wellner, Zoe (2018). "SIAM (Society for Industrial and Applied Mathematics)". SIAM Journal on Discrete Mathematics. 32: 591–610. arXiv:1701.04955. doi:10.1137/17m1116210. S2CID 43932757.
Niedermaier, Andrew; Rizzolo, Douglas; Su, Francis Edward (2014), "A tree Sperner lemma", in Barg, Alexander; Musin, Oleg R. (eds.), Discrete Geometry and Algebraic Combinatorics, Contemporary Mathematics, vol. 625, Providence, RI: American Mathematical Society, pp. 77–92, arXiv:0909.0339, doi:10.1090/conm/625/12492, ISBN 9781470409050, MR 3289406, S2CID 115157240
Mirzakhani, Maryam; Vondrák, Jan (2017), "Sperner's Colorings and Optimal Partitioning of the Simplex", in Loebl, Martin; Nešetřil, Jaroslav; Thomas, Robin (eds.), A Journey Through Discrete Mathematics: A Tribute to Jiří Matoušek, Cham: Springer International Publishing, pp. 615–631, arXiv:1611.08339, doi:10.1007/978-3-319-44479-6_25, ISBN 978-3-319-44479-6, S2CID 38668858, retrieved 2022-04-25
Gidea, Marian; Shmalo, Yitzchak (2018). "Combinatorial approach to detection of fixed points, periodic orbits, and symbolic dynamics". Discrete & Continuous Dynamical Systems - A. 38 (12). American Institute of Mathematical Sciences (AIMS): 6123–6148. arXiv:1706.08960. doi:10.3934/dcds.2018264. ISSN 1553-5231. S2CID 119130905.

siam.org (Global: 9,070^th place; English: 5,832^nd place)

epubs.siam.org

Asada, Megumi; Frick, Florian; Pisharody, Vivek; Polevy, Maxwell; Stoner, David; Tsang, Ling Hei; Wellner, Zoe (2018-01-01). "Fair Division and Generalizations of Sperner- and KKM-type Results". SIAM Journal on Discrete Mathematics. 32 (1): 591–610. arXiv:1701.04955. doi:10.1137/17M1116210. ISSN 0895-4801. S2CID 43932757.

worldcat.org (Global: 4^th place; English: 4^th place)

search.worldcat.org

McLennan, Andrew; Tourky, Rabee (2008). "Using Volume to Prove Sperner's Lemma". Economic Theory. 35 (3): 593–597. doi:10.1007/s00199-007-0257-0. ISSN 0938-2259. JSTOR 40282878.
Chen, Xi; Deng, Xiaotie (2009-10-17). "On the complexity of 2D discrete fixed point problem". Theoretical Computer Science. Automata, Languages and Programming (ICALP 2006). 410 (44): 4448–4456. doi:10.1016/j.tcs.2009.07.052. ISSN 0304-3975. S2CID 2831759.
Meunier, Frédéric (2006-10-01). "Sperner labellings: A combinatorial approach". Journal of Combinatorial Theory. Series A. 113 (7): 1462–1475. doi:10.1016/j.jcta.2006.01.006. ISSN 0097-3165.
Musin, Oleg R. (2015-05-01). "Extensions of Sperner and Tucker's lemma for manifolds". Journal of Combinatorial Theory. Series A. 132: 172–187. arXiv:1212.1899. doi:10.1016/j.jcta.2014.12.001. ISSN 0097-3165. S2CID 5699192.
Asada, Megumi; Frick, Florian; Pisharody, Vivek; Polevy, Maxwell; Stoner, David; Tsang, Ling Hei; Wellner, Zoe (2018-01-01). "Fair Division and Generalizations of Sperner- and KKM-type Results". SIAM Journal on Discrete Mathematics. 32 (1): 591–610. arXiv:1701.04955. doi:10.1137/17M1116210. ISSN 0895-4801. S2CID 43932757.
Wolsey, Laurence A (1977-07-01). "Cubical sperner lemmas as applications of generalized complementary pivoting". Journal of Combinatorial Theory. Series A. 23 (1): 78–87. doi:10.1016/0097-3165(77)90081-4. ISSN 0097-3165.
Brown, A. B.; Cairns, S. S. (1961-01-01). "Strengthening of Sperner's Lemma Applied to Homology Theory". Proceedings of the National Academy of Sciences. 47 (1): 113–114. Bibcode:1961PNAS...47..113B. doi:10.1073/pnas.47.1.113. ISSN 0027-8424. PMC 285253. PMID 16590803.
Gidea, Marian; Shmalo, Yitzchak (2018). "Combinatorial approach to detection of fixed points, periodic orbits, and symbolic dynamics". Discrete & Continuous Dynamical Systems - A. 38 (12). American Institute of Mathematical Sciences (AIMS): 6123–6148. arXiv:1706.08960. doi:10.3934/dcds.2018264. ISSN 1553-5231. S2CID 119130905.

Sperner's lemma (English Wikipedia)

adsabs.harvard.edu (Global: 14th place; English: 9th place)

ui.adsabs.harvard.edu

ams.org (Global: 434th place; English: 249th place)

mathscinet.ams.org

arxiv.org (Global: 49th place; English: 31st place)

claremont.edu (Global: low place; English: 6,768th place)