3 research outputs found
Regularity of Tor for weakly stable ideals
It is proved that if and are weakly stable ideals in a polynomial
ring , with a field, then the regularity of
has the expected upper bound. We also give a bound
for the regularity of for a weakly stable ideal
Rainbow Free Colorings and Rainbow Numbers for
An exact r-coloring of a set is a surjective function . A rainbow solution to an equation over is a solution
such that all components are a different color. We prove that every 3-coloring
of with an upper density greater than
contains a rainbow solution to . The rainbow number for an equation in
the set is the smallest integer such that every exact -coloring has
a rainbow solution. We compute the rainbow numbers of for the
equation , where is prime and