Geodesic
A Higman inequality for regular near polygons
Journal of Algebraic Combinatorics, Tome 34 (2011) no. 3, pp. 357-373.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: The inequality of Higman for generalized quadrangles of order $( s, t)$ with $s>1$ states that $t\leq s ^{2}$. We generalize this by proving that the intersection number $c _{ i }$ of a regular near $2 d$-gon of order $( s, t)$ with $s>1$ satisfies the tight bound $c _{ i }\leq ( s ^{2 i } - 1)/( s ^{2} - 1)$, 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 $2 d$-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.
Keywords: keywords distance-regular graphs, regular near polygons, dual polar graphs, hemisystems, classical parameters 
@article{JAC_2011__34_3_a6,
     author = {Vanhove, Fr\'ed\'eric},
     title = {A {Higman} inequality for regular near polygons},
     journal = {Journal of Algebraic Combinatorics},
     pages = {357--373},
     publisher = {mathdoc},
     volume = {34},
     number = {3},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2011__34_3_a6/}
}
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Vanhove, Frédéric. A Higman inequality for regular near polygons. Journal of Algebraic Combinatorics, Tome 34 (2011) no. 3, pp. 357-373. http://geodesic.mathdoc.fr/item/JAC_2011__34_3_a6/