Topic
Collatz conjecture
About: Collatz conjecture is a research topic. Over the lifetime, 1740 publications have been published within this topic receiving 23006 citations. The topic is also known as: 3n+1 conjecture & Ulam conjecture.
Papers published on a yearly basis
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Papers
Book•
1 Jan 2002
TL;DR: The L2-Betti numbers as mentioned in this paper are invariants of 3-manifolds of general spaces with group action, and the Singer Conjecture is one of the most well-known invariants.
Abstract: 0. Introduction.- 1. L2-Betti Numbers.- 2. Novikov-Shubin Invariants.- 3. L2-Torsion.- 4. L2-Invariants of 3-Manifolds.- 5. L2-Invariants of Symmetric Spaces.- 6. L2-Invariants for General Spaces with Group Action.- 7. Applications to Groups.- 8. The Algebra of Affiliated Operators.- 9. Middle Algebraic K-Theory and L-Theory of von Neumann Algebras.- 10. The Atiyah Conjecture.- 11. The Singer Conjecture.- 12. The Zero-in-the-Spectrum Conjecture.- 13. The Approximation Conjecture and the Determinant Conjecture.- 14. L2-Invariants and the Simplicial Volume.- 15. Survey on Other Topics Related to L2-Invariants.- 16. Solutions of the Exercises.- References.- Notation.
853 citations
Book•
1 Aug 2000
TL;DR: In this paper, the authors give an update survey of the most important results concerning the Jacobian conjecture: several equivalent descriptions are given and various related conjectures are discussed, and discuss the recent counter-examples, in all dimensions greater than two, to the Markus-Yamabe conjecture.
Abstract: In this paper we give an update survey of the most important results concerning the Jacobian conjecture: several equivalent descriptions are given and various related conjectures are discussed. At the end of the paper, we discuss the recent counter-examples, in all dimensions greater than two, to the Markus-Yamabe conjecture (Global asymptotic Jacobian conjecture). Resume Dans ce papier nous presentons un rapport actualise sur les resultats les plus importants concernant la conjecture Jacobienne : plusieurs formulations equivalentes et diverses conjectures connexes sont considerees. A la fin du papier, nous donnons les contre-exemples recents, en toute dimension plus grande que deux, a la conjecture de Markus-Yamabe.
800 citations
TL;DR: Kuperberg and Zeilberger as discussed by the authors proved that there are 1!4!7!...(3n-2)./n!/(n+1)!/.../(2n-1).
Abstract: Author(s): Kuperberg, Greg | Abstract: Robbins conjectured, and Zeilberger recently proved, that there are 1!4!7!...(3n-2)!/n!/(n+1)!/.../(2n-1)! alternating sign matrices of order n. We give a new proof of this result using an analysis of the six-vertex state model (also called square ice) based on the Yang-Baxter equation.
502 citations
443 citations
374 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2026 | 8 |
| 2025 | 496 |
| 2024 | 155 |
| 2023 | 151 |
| 2022 | 105 |
| 2021 | 62 |