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- W4296598206 abstract "For a matroid, its configuration determines its ({mathcal {G}})-invariant. Few examples are known of pairs of matroids with the same ({mathcal {G}})-invariant but different configurations. In order to produce new examples, we introduce the free m-cone (Q_m(M)) of a loopless matroid M, where m is a positive integer. We show that the ({mathcal {G}})-invariant of M determines the ({mathcal {G}})-invariant of (Q_m(M)), and that the configuration of (Q_m(M)) determines M; so if M and N are nonisomorphic and have the same ({mathcal {G}})-invariant, then (Q_m(M)) and (Q_m(N)) have the same ({mathcal {G}})-invariant but different configurations. We prove analogous results for several variants of the free m-cone. We also define a new matroid invariant of M, and show that it determines the Tutte polynomial of (Q_m(M))." @default.
- W4296598206 created "2022-09-22" @default.
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- W4296598206 date "2022-09-13" @default.
- W4296598206 modified "2023-10-17" @default.
- W4296598206 title "The Free m-Cone of a Matroid and Its $${mathcal {G}}$$-Invariant" @default.
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- W4296598206 doi "https://doi.org/10.1007/s00026-022-00606-2" @default.
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