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- W2894550712 abstract "To each cell e in a matroid M we can associate a non-negative integer ǁ e ǁ called the freedom of e. Geometrically the value ǁ e ǁ indicates how freely placed the cell is in the matroid. We see that ǁ e ǁ is equal to the degree of the modular cut generated by all the fully-dependent flats of M containing e. The relationship between freedom and basic matroid constructions, particularly one-point lifts and duality, is examined, and the applied to erections. We see that the number of times a matroid M can be erected is related to the degree of the modular cut generated by all the fully-dependent flats of M*. If ζ(M) is the set of integer polymatroids with underlying matroid structure M, then we show that for any cell e of M ǁ e ǁ= frac{max f (e)}{finzeta}We look at freedom in binary matroids and show that for a connected binary matroid M, ǁ e ǁ is the number of connected components of M/e. Finally the matroid join is examined and we are able to solve a conjecture of Lovasz and Recski that a connected binary matroid M is reducible if and only if there is a cell e of M with M/e disconnected." @default.
- W2894550712 created "2018-10-12" @default.
- W2894550712 creator A5047069160 @default.
- W2894550712 date "1981-01-01" @default.
- W2894550712 modified "2023-09-25" @default.
- W2894550712 title "Theory and applications of freedom in matroids" @default.
- W2894550712 doi "https://doi.org/10.21954/ou.ro.0000de47" @default.
- W2894550712 hasPublicationYear "1981" @default.
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