Notation, definitions and preliminaries Sample Clauses

Notation, definitions and preliminaries. The following notation will be used throughout the paper: n is the dimension of the complex space with the coordinate x; m is the number of rows in the matrix defining the Horn system; a2 b2 ν(a1, b1; a2, b2) ≡ ν a1 b1 is the index of the two vectors (a1, b1), (a2, b2) (see Definition 2.6); |m| = Σn mi and m! = m1! · · · mn! for m = (m1, . . . , mn); xm = xm1 · · · xmn for x = (x1, . . . , xn) and m = (m1, . . . , mn); Z≥0 is the set of non-negative integers, Z≤0 is the set of non-positive integers; Horn(ϕ) is the Horn hypergeometric system defined by the Ore–Sato coefficient ϕ (see Definition 2.3); Horn(A, c) stands for the Horn hypergeometric system defined by the Ore–Sato coefficient (2.2), where ti = 1 for all i = 1, . . . , n and U (s) 1 (see the construction after Definition 2.3); Ψ(ϕ) is
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