Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The width of a subset C of the vertices of a distance-regular graph is the maximum distance which occurs beten elements of C. Dually, the dual width of a subset in a cometric association scheme is the index of the "last" eigenspace in the Q-polynomial ordering to which the characteristic vector of C is not orthogonal. Elementary bounds are derived on these two new parameters.  show that any subset of minimal width is a completely regular code and that any subset of minimal dual width induces a cometric association scheme in the original. A variety of examples and applications are considered.
['Ae Andries Brouwer', 'Chris D. Godsil', 'Jack H. Koolen', 'William J. Martin']
I am writing a research paper on a idea Width and dual width of subsets in polynomial association schemes
[{"from": "human", "value": "I am writing a research paper on a idea Width and dual width of subsets in polynomial association schemes"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The width of a subset C of the vertices of a distance-regular graph is the maximum distance which occurs beten elements of C. Dually, the dual width of a subset in a cometric association scheme is the index of the \"last\" eigenspace in the Q-polynomial ordering to which the characteristic vector of C is not orthogonal. Elementary bounds are derived on these two new parameters.  show that any subset of minimal width is a completely regular code and that any subset of minimal dual width induces a cometric association scheme in the original. A variety of examples and applications are considered."}]