On Hall's conjecture
Andrej Dujella (2011)
Acta Arithmetica
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Andrej Dujella (2011)
Acta Arithmetica
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Dimitrov, Dimitar (2007)
Serdica Mathematical Journal
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2000 Mathematics Subject Classification: Primary 30C10, 30C15, 31B35. A challenging conjecture of Stephen Smale on geometry of polynomials is under discussion. We consider an interpretation which turns out to be an interesting problem on equilibrium of an electrostatic field that obeys the law of the logarithmic potential. This interplay allows us to study the quantities that appear in Smale’s conjecture for polynomials whose zeros belong to certain specific regions. A conjecture...
Pradipto Banerjee, Michael Filaseta (2010)
Acta Arithmetica
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G.L. Cohen, G.H. Smith (1988)
Elemente der Mathematik
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G. Grekos, L. Haddad, C. Helou, J. Pihko (2005)
Acta Arithmetica
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W. Narkiewicz (1977)
Colloquium Mathematicae
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András Biró (2003)
Acta Arithmetica
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G. Besson (2009)
Bollettino dell'Unione Matematica Italiana
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K. Inkeri (1976)
Acta Arithmetica
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Paule, Peter (1996)
Experimental Mathematics
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Fuzhen Zhang (2016)
Special Matrices
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We review and update on a few conjectures concerning matrix permanent that are easily stated, understood, and accessible to general math audience. They are: Soules permanent-on-top conjecture†, Lieb permanent dominance conjecture, Bapat and Sunder conjecture† on Hadamard product and diagonal entries, Chollet conjecture on Hadamard product, Marcus conjecture on permanent of permanents, and several other conjectures. Some of these conjectures are recently settled; some are still open.We...
K. Kubota (1977)
Acta Arithmetica
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P. D. T. A. Elliott (1976)
Colloquium Mathematicae
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C. Greither, Radan Kučera (2008)
Acta Arithmetica
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András Biró (2003)
Acta Arithmetica
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