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parallelConnection -- parallel connection of two matroids

Synopsis

Description

This function returns the parallel connection of two given matroids M and N (cf. Oxley, Section 7.1). Parallel connection is dual to seriesConnection: namely, the parallel connection of M and N is the dual of the series connection of M* and N*.

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 parallel connection using a different basepoint, one can first relabel M and/or N.)

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 : parallelConnection(M, uniformMatroid(1,2))

o3 = a "matroid" of rank 6 on 14 elements

o3 : Matroid

See also

Ways to use parallelConnection :

For the programmer

The object parallelConnection is a method function.