On the circuits of splitting matroids representable over GF(p)

We apply the splitting operation defined on binary matroids (Raghunathan et al., 1998) to \(p\)- matroids, where \(p\)-matroids refer to matroids representable over \(GF(p).\) We also characterize circuits, bases, and independent sets of the resulting matroid. Sufficient conditions to yield Eulerian \(p\)-matroids from Eulerian and non-Eulerian \(p\)-matroids by applying the splitting operation are obtained. A class of connected \(p\)-matroids that gives connected \(p\)-matroids under the splitting operation is characterized. In Application, we characterize a class of paving \(p\)-matroids, which produces paving matroids after the splitting operation.