Obstacles to decomposition theorems for sixth-root-of-unity matroids. (English) Zbl 1310.05042

Chun, Carolyn; Mayhew, Dillon; Newman, Mike

Ann. Comb. 19, No. 1, 79-93 (2015).

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

Keywords:

matroids; partial field; decomposition theorem

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