Multiple sums and generating functions.
L. Carlitz (1965)
Collectanea Mathematica
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L. Carlitz (1965)
Collectanea Mathematica
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Roman Sikorski (1961)
Studia Mathematica
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Shah, Manilal (1972)
Portugaliae mathematica
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Manilal Shah (1976)
Gaceta Matemática
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R. Ramírez, N. Sadovskaia (1996)
Collectanea Mathematica
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The aim of this paper is to construct the analytic vector fields with given as trajectories or solutions. In particular we construct the polynomial vector field from given conics (ellipses, hyperbola, parabola, straight lines) and determine the differential equations from a finite number of solutions.
Breves Filho, J.A. (1974)
Portugaliae mathematica
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Roman Sikorski (1961)
Studia Mathematica
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S. Peter Farbman (1995)
Publicacions Matemàtiques
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The question of whether two parabolic elements A, B of SL(C) are a free basis for the group they generate is considered. Some known results are generalized, using the parameter τ = tr(AB) - 2. If τ = a/b ∈ Q, |τ| < 4, and |a| ≤ 16, then the group is not free. If the subgroup generated by b in Z / aZ has a set of representatives, each of which divides one of b ± 1, then the subgroup of SL(C) will not be free.
E. R. Hedrick (1928)
Journal de Mathématiques Pures et Appliquées
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Manilal Shah (1975)
Gaceta Matemática
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