
Quartic rationally derived polynomials ★★★
Author(s): Buchholz; MacDougall
Call a polynomial rationally derived if all roots of
and the nonzero derivatives of
are rational.
Conjecture There does not exist a quartic rationally derived polynomial
with four distinct roots.
![$ p \in {\mathbb Q}[x] $](/files/tex/a72fcb0a006c3c2afb3ba69722ccdb2599b83e90.png)
Keywords: derivative; diophantine; elliptic; polynomial
Partial List Coloring ★★★
Author(s): Iradmusa
Let be a simple graph, and for every list assignment
let
be the maximum number of vertices of
which are colorable with respect to
. Define
, where the minimum is taken over all list assignments
with
for all
.
Conjecture [2] Let
be a graph with list chromatic number
and
. Then



![\[\frac{\lambda_r}{r}\geq\frac{\lambda_s}{s}.\]](/files/tex/47be18e956355dd433b88b66eabf01a9e3ed5f61.png)
Keywords: list assignment; list coloring
Is every regular paratopological group Tychonoff? ★★
Author(s): unknown
Question Is every regular paratopological group Tychonoff?
Keywords: paratopological group; Tychonoff; Tychonoff space