scholarly journals Hochster's theta invariant and the Hodge–Riemann bilinear relations

2011 ◽  
Vol 226 (2) ◽  
pp. 1692-1714 ◽  
Author(s):  
W. Frank Moore ◽  
Greg Piepmeyer ◽  
Sandra Spiroff ◽  
Mark E. Walker
Keyword(s):  
Bilinear Relations

Bilinear Relations

1992 ◽  
pp. 77-83
Author(s):  
Raghavan Narasimhan
Keyword(s):  
Bilinear Relations

scholarly journals Special polynomials and the Hirota Bilinear relations of the second and the fourth Painlevé equations

2000 ◽  
Vol 159 ◽  
pp. 179-200 ◽  
Author(s):  
Satoshi Fukutani ◽  
Kazuo Okamoto ◽  
Hiroshi Umemura
Keyword(s):  
Recurrence Relation ◽  
Rational Functions ◽  
Painlevé Equations ◽  
Algebraic Proof ◽  
Painleve Equations ◽  
Special Polynomials ◽  
Bilinear Relations ◽  
Hirota Bilinear

We give a purely algebraic proof that the rational functions Pn(t), Qn(t) inductively defined by the recurrence relation (1), (2) respectively, are polynomials. The proof reveals the Hirota bilinear relations satisfied by the τ-functions.

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