Number Theory » Additive N.T.

DIS-PROOF OF BEALS CONJECTURE ★★★

Author(s):

If A(pwr)x+B(pwr)y=C(pwr)z where A,B,C,x,y,z are positive integers and x,y,z>=2,then A,B,C must have a common prime factor.

Keywords: beals conjecture

Posted by lalitha
updated April 24th, 2013
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Algebra

Sub-atomic product of funcoids is a categorical product ★★

Author(s):

Conjecture   In the category of continuous funcoids (defined similarly to the category of topological spaces) the following is a direct categorical product:
    \item Product morphism is defined similarly to the category of topological spaces. \item Product object is the sub-atomic product. \item Projections are sub-atomic projections.

See details, exact definitions, and attempted proofs here.

Keywords:

Posted by porton
updated April 21st, 2013
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Graph Theory » Coloring » Vertex coloring

Bounding the on-line choice number in terms of the choice number ★★

Author(s): Zhu

Question   Are there graphs for which $ \text{ch}^{\text{OL}}-\text{ch} $ is arbitrarily large?

Keywords: choosability; list coloring; on-line choosability

Posted by Jon Noel
updated April 11th, 2013
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