A Higman inequality for regular near polygons

作者：Vanhove Frederic^*

来源：Journal of Algebraic Combinatorics, 2011, 34(3): 357-373.

DOI：10.1007/s10801-011-0275-7

• Distance-regular graphs
• Regular near polygons
• Dual polar graphs
• Hemisystems
• Classical parameters

The inequality of Higman for generalized quadrangles of order (s,t) with s > 1 states that ta parts per thousand currency signs (2). We generalize this by proving that the intersection number c (i) of a regular near 2d-gon of order (s,t) with s > 1 satisfies the tight bound c (i) a parts per thousand currency sign(s (2i) -1)/(s (2)-1), and we give properties in case of equality. It is known that hemisystems in generalized quadrangles meeting the Higman bound induce strongly regular subgraphs. We also generalize this by proving that a similar subset in regular near 2d-gons meeting the bounds would induce a distance-regular graph with classical parameters (d,b,alpha,beta)=(d,-q,-(q+1)/2,-((-q) (d) +1)/2) with q an odd prime power.

• 出版日期2011-11