Abstract
We introduce the family of B 2-type arrangements as a generalization of the classical Coxeter arrangement of type B 2 and consider the stability and the freeness of it. We show the freeness and (semi)stability are determined by the combinatorics. Moreover, we give a partial answer to the 4-shift problem, which is a conjecture on the combinatorics and geometry induced from the B 2-type arrangements.
2000 Mathematics Subject Classification:
ACKNOWLEDGMENT
The author is grateful to the referee for the careful reading of this article and a lot of useful suggestions.
Notes
Communicated by S. Goto.