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This is a preliminary draft of Chapters 1-3 of our forthcoming textbook "Introduction to Cluster Algebras." This installment contains: Chapter 1.
Über variationsvermindernde lineare Transformationen
Schoenberg, I · 1930
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Oscillation matrices and kernels and small vibrations of mechanical systems
Gantmacher, F. P., and Krein, M. G · 1941
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A reduction theorem for totally positive matrices
Whitney, A. M · 1952
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On totally positive matrices
Loewner, C · 1955
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Teilungen der Ebene durch Geraden oder topologische Geraden
Ringel, G · 1956
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A treatise on the theory of determinants
Muir, T · 1960
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Homotopy associativity of H H -spaces. I, II
Stasheff, J. D · 1963
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Frieze patterns
Coxeter, H. S. M · 1971
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Integral matrices
Newman, M · 1972
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Coxeter functors, and Gabriel’s theorem
Bernšteĭn, I. N., Gel ′ · 1973
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The L U LU -factorization of totally positive matrices
Cryer, C. W · 1973
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Some properties of totally positive matrices
Cryer, C. W · 1976
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The invariant theory of binary forms
Kung, J. P. S., and Rota, G.-C · 1984
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The decorated Teichmüller space of punctured surfaces
Penner, R. C · 1987
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On the thermodynamic Bethe ansatz equations for reflectionless A D E ADE scattering theories
Zamolodchikov, A. B · 1991
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The pentagram map
Schwartz, R · 1992
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On classification of N = 2 N=2 supersymmetric theories
Cecotti, S., and Vafa, C · 1993
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The mathematical pamphlets of Charles Lutwidge Dodgson and related pieces
Dodgson, C. L · 1994
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Total positivity in reductive groups
Lusztig, G · 1994
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Electric-magnetic duality in supersymmetric non-abelian gauge theories
Seiberg, N · 1995
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Parametrizations of canonical bases and totally positive matrices
Berenstein, A., Fomin, S., and Zelevinsky, A · 1996
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Non-Euclidean geometry
Coxeter, H. S. M · 1998
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Introduction to total positivity
Lusztig, G · 1998
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Double Bruhat cells and total positivity
Fomin, S., and Zelevinsky, A · 1999
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Total positivity: tests and parametrizations
Fomin, S., and Zelevinsky, A · 2000
Dual Teichmüller and lamination spaces
Fock, V. V., and Goncharov, A. B · 2007
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Root systems and generalized associahedra
Fomin, S., and Reading, N · 2007
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Laurent polynomials and superintegrable maps
Hone, A. N. W · 2007
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Perfect matchings and the octahedron recurrence
Speyer, D. E · 2007
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Mutation classes of skew-symmetric 3 × 3 3\times 3 -matrices
Assem, I., Blais, M., Brüstle, T., and Samson, A · 2008
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Introduction to Cluster Algebras. Chapter 6
Fomin, S., and Williams, L · 2008
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Cited alongside, same era.
Totally nonnegative and oscillatory elements in semisimple groups
Fomin, S., and Zelevinsky, A · 2000
Cited alongside, same era.
Trees and matchings
Kenyon, R. W., Propp, J. G., and Wilson, D. B · 2000
Cited alongside, same era.
Toric duality as Seiberg duality and brane diamonds
Feng, B., Hanany, A., He, Y.-H., and Uranga, A. M · 2001
Cited alongside, same era.
Cluster algebras. I. Foundations
Fomin, S., and Zelevinsky, A · 2002
Cited alongside, same era.
Cluster algebras. II. Finite type classification
Fomin, S., and Zelevinsky, A · 2003
Cited alongside, same era.
Integrality and the Laurent phenomenon for Somos 4 and Somos 5 sequences
Hone, A. N. W., and Swart, C · 2008
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Algorithms in invariant theory
Sturmfels, B · 2008
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Perfect matchings for the three-term Gale-Robinson sequences
Bousquet-Mélou, M., Propp, J., and West, J · 2009
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Total positivity and cluster algebras
Fomin, S · 2010
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Motivic Donaldson-Thomas invariants: summary of results
Kontsevich, M., and Soibelman, Y · 2010
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Cluster mutation-periodic quivers and associated Laurent sequences
Fordy, A. P., and Marsh, B · 2011
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The pentagram map and Y Y -patterns
Glick, M · 2011
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Perspectives on projective geometry
Richter-Gebert, J · 2011
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Markov’s theorem and 100 years of the uniqueness conjecture
Aigner, M · 2013
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Dimers and cluster integrable systems
Goncharov, A. B., and Kenyon, R · 2013
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Mutation classes of skew-symmetrizable 3 × 3 3\times 3 matrices
Seven, A. I · 2013
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