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seriesConnection -- series connection of two matroids

Synopsis

Description

This function returns the series connection of two given matroids M and N (cf. Oxley, Section 7.1).

It is always assumed that the common basepoint of M and N is the first element in the respective ground sets, i.e. the element with index 0. (To form a series connection using a different basepoint, one can first relabel M and/or N.)

This method includes series extensions as a special case: a series extension of M is a series connection of M with U(1,2).

i1 : G = graph({{0,1},{1,2},{2,3},{3,4},{4,5},{5,6},{6,0},{0,2},{0,3},{0,4},{1,3},{3,5},{3,6}})

o1 = Graph{0 => {1, 2, 3, 4, 6}   }
           1 => {0, 2, 3}
           2 => {0, 1, 3}
           3 => {0, 1, 2, 4, 5, 6}
           4 => {0, 3, 5}
           5 => {3, 4, 6}
           6 => {0, 3, 5}

o1 : Graph
 
i2 : M = matroid G

o2 = a "matroid" of rank 6 on 13 elements

o2 : Matroid
 
i3 : seriesConnection(M, uniformMatroid(1,2))

o3 = a "matroid" of rank 7 on 14 elements

o3 : Matroid

See also

Ways to use seriesConnection :

For the programmer

The object seriesConnection is a method function.