×

zbMATH — the first resource for mathematics

Obstacles to decomposition theorems for sixth-root-of-unity matroids. (English) Zbl 1310.05042
Summary: We construct an infinite family of highly connected sixth-root-of-unity matroids that are not near-regular. This family is an obstacle to any decomposition theorem for sixth-root-of-unity matroids in terms of near-regular matroids.

MSC:
05B35 Combinatorial aspects of matroids and geometric lattices
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Geelen, J.; Oxley, J.; Vertigan, D.; Whittle, G., Weak maps and stabilizers of classes of matroids, Adv. Appl. Math., 21, 305-341, (1998) · Zbl 0919.05010
[2] Geelen, J.; Oxley, J.; Vertigan, D.; Whittle, G., Totally free expansions of matroids, J. Combin. Theory Ser. B, 84, 130-179, (2002) · Zbl 1048.05020
[3] Hall, R.; Mayhew, D.; Zwam, S.H.M., The excluded minors for near-regular matroids, European J. Combin., 32, 802-830, (2011) · Zbl 1227.05114
[4] Mayhew, D.; Whittle, G.; Zwam, S.H.M., An obstacle to a decomposition theorem for near-regular matroids, SIAM J. Discrete Math., 25, 271-279, (2011) · Zbl 1290.05057
[5] Oxley J.: Matroid Theory. Second edition. Oxford University Press, New York (2011) · Zbl 1254.05002
[6] Pendavingh, R.A.; Zwam, S.H.M., Lifts of matroid representations over partial fields, J. Combin. Theory Ser. B, 100, 36-67, (2010) · Zbl 1215.05024
[7] Seymour, P.D., Decomposition of regular matroids, J. Combin. Theory Ser. B, 28, 305-359, (1980) · Zbl 0443.05027
[8] Slilaty, D.: Personal communication. · Zbl 0443.05027
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.