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On the "Section Conjecture" in anabelian geometry
Published 2003“…It disproves both conjectures for the field of real or p-adic algebraic numbers. …”
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62
Graphical calculi and their conjecture synthesis
Published 2020“…The initial aim for this was Conjecture Synthesis; the algorithmic process of creating theorems. …”
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63
On the KŁR conjecture in random graphs
Published 2015“…We prove a variant of this conjecture which is sufficient for most known applications to random graphs. …”
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64
Alperin's conjecture for algebraic groups
Published 2008“…We prove analogues for reductive algebraic groups of some results for finite groups due to Knörr and Robinson from 'Some remarks on a conjecture of Alperin', J. London Math. Soc (2) 39 (1989), 48-60, which play a central rôle in their reformulation of Alperin's conjecture for finite groups. © 2007. …”
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Proving the Herman-Protocol Conjecture
Published 2016“…In this paper, we prove McIver and Morgan's conjecture and establish that h = 4/27 is indeed optimal.…”
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On the Skolem problem and the Skolem conjecture
Published 2022“…</p> <p>Second, assuming the Skolem Conjecture (a central hypothesis in Diophantine analysis, also known as the Exponential Local-Global Principle), we show that the Skolem Problem for LRS of order 5 is decidable, and exhibit a concrete procedure for solving it.…”
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Proof of the Kalai-Meshulam conjecture
Published 2020“…We prove this conjecture.</p>…”
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LERF and the Lubotzky-Sarnak conjecture
Published 2008“…This is used to show that, if in addition the fundamental group of the manifold is LERF, then it satisfies the Lubotzky-Sarnak conjecture.…”
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A Reduction of the Graph Reconstruction Conjecture
Published 2014-08-01“…A graph is said to be reconstructible if it is determined up to isomor- phism from the collection of all its one-vertex deleted unlabeled subgraphs. Reconstruction Conjecture (RC) asserts that all graphs on at least three vertices are reconstructible. …”
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A FORMAL PROOF OF THE KEPLER CONJECTURE
Published 2017-01-01“…This article describes a formal proof of the Kepler conjecture on dense sphere packings in a combination of the HOL Light and Isabelle proof assistants. …”
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78
Alperin weight conjecture and related developments
Published 2022-12-01Subjects: “…Alperin weight conjecture…”
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79
Empowering Polynomial Theory Conjectures with Spreadsheets
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80
The equivalence of several conjectures on independence of $\ell$
Published 2020-11-01“…We consider several conjectures on the independence of $\ell$ of the \'etale cohomology of (singular, open) varieties over $\bar{\mathbf F}_p$. …”
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