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On Valuations, the Characteristic Polynomial, and Complex Subspace Arrangements by Richard Ehrenborg; Margaret A. Readdy is a Mathematics article available to read on EtoBox.
What is On Valuations, the Characteristic Polynomial, and Complex Subspace Arrangements about?
We present a new combinatorial method to determine the characteristic polynomial of any subspace arrangement that is defined over an infinite field, generalizing the work of Blass and Sagan. Our methods stem from the theory of valuations and Groemer's integral theorem. As a corollary of our main theorem, we obtain a result of Zaslavsky about the number of chambers of a real hyperplane arrangement. The examples we consider include a family of complex subspace arrangements, which we call the divisor Dowling arrangement, whose intersection lattice generalizes that of the Dowling lattice. We also determine the characteristic polynomial of interpolations between subarrangements of the divisor Dowling arrangement, generalizing the work of Jo zefiak and Sagan.
Who reads On Valuations, the Characteristic Polynomial, and Complex Subspace Arrangements?
It is typically read by researchers, students, and practitioners in Mathematics.
- Author
- Richard Ehrenborg; Margaret A. Readdy
- Publisher
- Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0001-8708)
- Published
- 1998
- Language
- EN
- Field
- Mathematics (Physical Sciences)