The characteristic quasi-polynomials of the arrangements of root systems and mid-hyperplane arrangements

Details The characteristic quasi-polynomials of the arrangements of root systems and mid-hyperplane arrangements The characteristic quasi-polynomials of the arrangements of root systems and mid-hyperplane arrangements

2007-07-10

arxiv.org/abs/0707.1381v3

Progress in Math. 283, Arrangements, local systems and singularities, (ed. F. Elzein, A. Suciu, M. Tosun, A. M. Uludag, S. Y

Mathematics

Combinatorics

Scientific paper

Let $q$ be a positive integer. In our recent paper, we proved that the cardinality of the complement of an integral arrangement, after the modulo $q$ reduction, is a quasi-polynomial of $q$, which we call the characteristic quasi-polynomial. In this paper, we study general properties of the characteristic quasi-polynomial as well as discuss two important examples: the arrangements of reflecting hyperplanes arising from irreducible root systems and the mid-hyperplane arrangements. In the root system case, we present a beautiful formula for the generating function of the characteristic quasi-polynomial which has been essentially obtained by Ch. Athanasiadis and by A. Blass and B. Sagan. On the other hand, it is hard to find the generating function of the characteristic quasi-polynomial in the mid-hyperplane arrangement case. We determine them when the dimension is less than six.

Affiliated with

Also associated with

No associations

Rating

The characteristic quasi-polynomials of the arrangements of root systems and mid-hyperplane arrangements does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The characteristic quasi-polynomials of the arrangements of root systems and mid-hyperplane arrangements, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The characteristic quasi-polynomials of the arrangements of root systems and mid-hyperplane arrangements will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-453413