# parallelConnection -- parallel connection of two matroids

## Synopsis

• Usage:
parallelConnection(M, N)
• Inputs:
• M, ,
• N, ,
• Outputs:
• , the parallel connection of M and N with basepoint 0

## 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