Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Let            B  =    ∪    i  =  1    n      B    i          be a partition of base   B     B        in the union (or sum) of   n     n        matroids into independent sets   B i        B    i          of   M i        M    i         .  prove that every other base   B ′        B    ′          has such a partition where   B i        B    i          and              B    i    ′          span the same set in   M i        M    i          for   i=1,2,…,n     i  =  1  ,  2  ,  …  ,  n       .
['Csongor György Csehi', 'András Recski']
I am writing a research paper on a idea Partitioning the bases of the union of matroids
[{"from": "human", "value": "I am writing a research paper on a idea Partitioning the bases of the union of matroids"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Let            B  =    \u222a    i  =  1    n      B    i          be a partition of base   B     B        in the union (or sum) of   n     n        matroids into independent sets   B i        B    i          of   M i        M    i         .  prove that every other base   B \u2032        B    \u2032          has such a partition where   B i        B    i          and              B    i    \u2032          span the same set in   M i        M    i          for   i=1,2,\u2026,n     i  =  1  ,  2  ,  \u2026  ,  n       ."}]