Classification conjecture for maximum -EKR sets in dual polar graphs
Classification conjecture for maximum -EKR sets in dual polar graphs
Let be a maximum-size -EKR set of generators in a polar space of rank and type parameter , meaning that any two members of meet in dimension at least . A maximum -EKR set classification conjecture. One of the following cases occurs:
- is the set of all generators on a fixed -space.
- is even, and is the set of all generators meeting a fixed generator in dimension at least .
- is odd, and is the set of all generators meeting a fixed -dimensional space in dimension at least .
- , , is odd, and is the largest example for described by the cited reference.
This conjecture seeks a complete classification of maximum -EKR sets, extending known classifications in special cases. The proposed families arise from the natural geometric configurations of generators; the general classification remains open in the source.
Sources & referencesView supporting material
Primary source
Ferdinand Ihringer and Klaus Metsch, “Large \0, 1, , t\-Cliques in Dual Polar Graphs”, arXiv:1510.01697 (2015).
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