Gröbner Deformations of Hypergeometric Differential Equations

Abstract

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Binomial residues

“…Formulas and algorithms for computing binomial residues are presented in §4. In §5, we complete the proof of Theorem 1.1, and we prove Conjecture 5.7 from our previous paper [8] [12], [18] [5], [6], [10]. This will allow us in §5 to find bases of A-hypergeometric stable rational functions for Lawrence liftings in terms of binomial residues, and to give a geometric meaning to the linear dependencies among binomial residues.…”

“…In the notation of [11], [12], [18] [21], it counts the regions of the hyperplane arrangement (2.5). Lemma [5], [6].…”

Gevrey Expansions of Hypergeometric Integrals I

“…It is proved in [SST,Proposition 3.4.13] that the formal expression ϕ v is annihilated by the hypergeometric ideal H A (β) if and only if the negative support of v is minimal, which means that there is no u ∈ ker Z (A) with nsupp(v + u) nsupp(v).…”

Computing the integer programming gap

“…If c is generic then M(A, c) is an initial ideal of the toric ideal of A; see [16]. If c is not generic then we can compute M(A, c) using [14,Algorithm 4.4.2]. A monomial ideal I in R[x 1 , .…”