一类平面直线构形的Falk不变量  

Falk's invariant for a class of line arrangements

作　　者：孙雪梅[1] 郭玲[1] 张林[1] 姜广峰[1] 

机构地区：[1]北京化工大学理学院,北京100029

出　　处：《北京化工大学学报（自然科学版）》2013年第B12期100-105,共6页Journal of Beijing University of Chemical Technology(Natural Science Edition)

基　　金：国家自然科学基金(11071010)

摘　　要：针对二维非中心构形的Falk不变量进行了研究。对一类特殊的线构形A:A中任意4个重数大于2的交点都不构成一个K4构形,且任意3个重数大于2的交点都不在一条直线上,证明了其Falk不变量等于长度为3的极小圈个数的2倍,部分地回答了关于Falk不变量的组合学解释问题。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.

关 键 词：超平面构形 Falk不变量 非中心构形 直线构形 

分 类 号：O157[理学—数学]