#Counterexample

Latest posts tagged with #Counterexample on Bluesky

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Posts tagged #Counterexample

Alexander Kasprzyk

@amkasprzyk.bsky.social

3 months ago

ACC for F-Signature: A Likely Counterexample Let k=\bar{F}_2 and let 0\neq \alpha\in k. We present a conjecture supported by computer experimentation involving the Brenner–Monsky quartic g_\alpha=\alpha x^2 y^2 + z^4 + xyz^2 + (x^3 + y^3)z \in k[[x,y,z]]. If true, this conjecture provides a formula for the Hilbert–Kunz multiplicity and F-signature of the family of four-dimensional hypersurfaces defined by uv + g_\alpha \in k[[x,y,z,u,v]] which depends on [F_2(\alpha):F_2], giving an infinite increasing chain of strict inequalities of F-signatures. Additionally, we obtain for any t\in N a formula for the Hilbert–Kunz multiplicity and F-signature of the t-parameter family of (3t+1)–dimensional hypersurfaces defined by uv + \sum_{i]1+^t g_{\alpha_i}g_{\alpha_i}(x_i,y_i,z_i).

"ACC for F-Signature: A Likely Counterexample" by Clay Adams, Theodore J. Sandstrom, and Austyn Simpson. #ExperimentalMath #Counterexample #MathSky

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ScienceHumor.io

@sciencehumor-io.bsky.social

6 months ago

Why Didn't I Think Of That?

Why Didn't I Think Of That?

#Mathematics #Academia #Research #Proofs #Counterexample

sciencehumor.io/math-memes/why-didnt-i-t...

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Alexander Kasprzyk

@amkasprzyk.bsky.social

7 months ago

Confirming Brennan’s Conjecture Numerically on a Counterexample to Thurston’s K = 2 Conjecture It was shown by Bishop that if Thurston’s K = 2 conjecture holds for some planar domain, then Brennan’s conjecture holds for the Riemann map of that domain as well. In this paper we show numerically that the original counterexample to Thurston’s K = 2 conjecture given by Epstein, Marden and Marković is not a counterexample to Brennan’s conjecture.

"Confirming Brennan’s Conjecture Numerically on a Counterexample to Thurston’s K = 2 Conjecture" by Ognjen Tošić. #ExperimentalMath #Counterexample #MathSky

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iMathTutor®

@imathtutor.bsky.social

8 months ago

#mathematics #math #topology #MetricSpace #Counterexample
Source:https://buff.ly/zh3L4tJ

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