Displaying similar documents to “Mycielski-Sierpiński conjecture and Korec-Znám result”

An update on a few permanent conjectures

Fuzhen Zhang (2016)

Special Matrices

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We review and update on a few conjectures concerning matrix permanent that are easily stated, understood, and accessible to general math audience. They are: Soules permanent-on-top conjecture†, Lieb permanent dominance conjecture, Bapat and Sunder conjecture† on Hadamard product and diagonal entries, Chollet conjecture on Hadamard product, Marcus conjecture on permanent of permanents, and several other conjectures. Some of these conjectures are recently settled; some are still open.We...

On the Collatz conjecture

Sebastian Hebda (2013)

Colloquium Mathematicae

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We propose two conjectures which imply the Collatz conjecture. We give a numerical evidence for the second conjecture.

Around Podewski's conjecture

Krzysztof Krupiński, Predrag Tanović, Frank O. Wagner (2013)

Fundamenta Mathematicae

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A long-standing conjecture of Podewski states that every minimal field is algebraically closed. Known in positive characteristic, it remains wide open in characteristic zero. We reduce Podewski's conjecture to the (partially) ordered case, and we conjecture that such fields do not exist. We prove the conjecture in case the incomparability relation is transitive (the almost linear case). We also study minimal groups with a (partial) order, and give a complete classification...

Thinnest Covering of the Euclidean Plane with Incongruent Circles

Dietmar Dorninger (2017)

Analysis and Geometry in Metric Spaces

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In 1958 L. Fejes Tóth and J. Molnar proposed a conjecture about a lower bound for the thinnest covering of the plane by circles with arbitrary radii from a given interval of the reals. If only two kinds of radii can occur this conjecture was in essence proven by A. Florian in 1962, leaving the general case unanswered till now. The goal of this paper is to analytically describe the general case in such a way that the conjecture can easily be numerically verified and upper and lower limits...