### Abstract

The problem of finding the principal partition of a parity matroid is shown to be polynomially unsolvable in general. Two theorems are refined by using the concept of a minimal central minor: the first is the theorem on the existence of the principal partition; the second is the theorem on the characterization of the maximum independent parity set of a matroid with principal partition. A new polynomially solvable class of the parity problem is presented. Also, the weighted parity problem of a matroid with a principal partition is shown to be polynomially unsolvable in general. Finally, the concept of the principal partition for a parity matroid is generalized to a parity polymatroid.

Original language | English |
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Pages (from-to) | 815-818 |

Number of pages | 4 |

Journal | Proceedings - IEEE International Symposium on Circuits and Systems |

Publication status | Published - 1985 Dec 1 |

### ASJC Scopus subject areas

- Electrical and Electronic Engineering

## Cite this

*Proceedings - IEEE International Symposium on Circuits and Systems*, 815-818.