Read's conjecture
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Short description: Mathematical theorem first conjectured by Ronald Read
Read's conjecture is a conjecture, first made by Ronald Read, about the unimodality of the coefficients of chromatic polynomials in the context of graph theory.[1][2] In 1974, S. G. Hoggar tightened this to the conjecture that the coefficients must be strongly log-concave. Hoggar's version of the conjecture is called the Read–Hoggar conjecture.[3][4]
The Read–Hoggar conjecture had been unresolved for more than 40 years before June Huh proved it in 2009, during his PhD studies, using methods from algebraic geometry.[1][5][6][7]
References
- ↑ 1.0 1.1 Baker, Matthew (January 2018). "Hodge theory in combinatorics" (in en). Bulletin of the American Mathematical Society 55 (1): 57–80. doi:10.1090/bull/1599. ISSN 0273-0979. https://www.ams.org/bull/2018-55-01/S0273-0979-2017-01599-6/.
- ↑ R. C. Read, An introduction to chromatic polynomials, J. Combinatorial Theory 4 (1968), 52–71. MR0224505 (37:104)
- ↑ Hoggar, S. G (1974-06-01). "Chromatic polynomials and logarithmic concavity" (in en). Journal of Combinatorial Theory. Series B 16 (3): 248–254. doi:10.1016/0095-8956(74)90071-9. ISSN 0095-8956.
- ↑ Huh, June. "Hard Lefschetz theorem and Hodge-Riemann relations for combinatorial geometries". https://web.northeastern.edu/martsinkovsky/p/rtrt/20152016/huh-slides.pdf.
- ↑ "He Dropped Out to Become a Poet. Now He's Won a Fields Medal." (in en). Quanta Magazine. 5 July 2022. https://www.quantamagazine.org/june-huh-high-school-dropout-wins-the-fields-medal-20220705. Retrieved 5 July 2022.
- ↑ Kalai, Gil (July 2022). "The Work of June Huh". Proceedings of the International Congress of Mathematicians 2022: 1–16. https://www.mathunion.org/fileadmin/IMU/Prizes/Fields/2022/laudatio-jh.pdf., pp. 2–4.
- ↑ Huh, June (2012). "Milnor numbers of projective hypersurfaces and the chromatic polynomial of graphs". Journal of the American Mathematical Society 25: 907—927. doi:10.1090/S0894-0347-2012-00731-0.
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