Falk’s invariant for a class of line arrangements

SUN XueMei;GUO Ling;ZHANG Lin;JIANG GuangFeng

Journal of Beijing University of Chemical Technology ›› 2013, Vol. 40 ›› Issue (增刊) : 100-105.

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Journal of Beijing University of Chemical Technology ›› 2013, Vol. 40 ›› Issue (增刊) : 100-105.
管理与数理科学

Falk’s invariant for a class of line arrangements

  • SUN XueMei;GUO Ling;ZHANG Lin;JIANG GuangFeng
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Abstract

In this paper, we studied Falk’s invariant for a special class of line arrangements in a projective plane. The results show that if a line arrangement does not contain the K4 arrangement as its subarrangement, and no line contains three intersections points with the multiplicity greater than 2, then Falk’s invariant equals twice the number of circuits of length 3. This partially answers an open question about the combinatorial interpretation of Falk’s invariant for non-graphic arrangements.

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SUN XueMei;GUO Ling;ZHANG Lin;JIANG GuangFeng. Falk’s invariant for a class of line arrangements[J]. Journal of Beijing University of Chemical Technology, 2013, 40(增刊): 100-105

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