TY - JOUR

T1 - On Valuations, the Characteristic Polynomial, and Complex Subspace Arrangements

AU - Ehrenborg, Richard

AU - Readdy, Margaret A.

PY - 1998/3/1

Y1 - 1998/3/1

N2 - 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 Józefiak and Sagan.

AB - 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 Józefiak and Sagan.

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U2 - 10.1006/aima.1997.1693

DO - 10.1006/aima.1997.1693

M3 - Article

AN - SCOPUS:0002358389

SN - 0001-8708

VL - 134

SP - 32

EP - 42

JO - Advances in Mathematics

JF - Advances in Mathematics

IS - 1

ER -