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Titlebook: Quadratic Forms; Combinatorics and Nu Michael Barot,Jesús Arturo Jiménez González,José-A Book 2019 Springer Nature Switzerland AG 2019 inte

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Quadratic Forms978-3-030-05627-8Series ISSN 1572-5553 Series E-ISSN 2192-2950
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Book 2019 of algebras and derived categories. ..Some of these beautiful results remain practically unknown to students and scholars, and are scattered in papers written between 1970 and the present day. Besides the many classical results, the book also encompasses a few new results and generalizations...The
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Nonnegative Quadratic Forms,ot induced form, and . is a .-root induced form. Here we show that two non-negative semi-unit forms have the same Dynkin type if and only if they are root equivalent, and derive an interesting partial order in the set of Dynkin types.
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Fundamental Concepts,ctor . in . are said to be . by ., and the form . is said to be . if every positive integer is represented by .. We sketch the proof of Conway and Schneeberger’s ., which states that a positive integral form with associated symmetric matrix having integer coefficients is universal if and only if it
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Positive Quadratic Forms,gral quadratic unit forms . with .(.) > 0 for any nonzero vector . in .. A unit form . is . if it is not positive, but each proper restriction of . is. A vector . is called . for . if .(. + .) = .(.) for any vector . in .. We prove Ovsienko’s Criterion: a unit form in . ≥ 3 variables is critical non
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