Lattice path matroids: the excluded minors. (English) Zbl 1231.05054
Summary: A lattice path matroid is a transversal matroid for which some antichain of intervals in some linear order on the ground set is a presentation. We characterize the minor-closed class of lattice path matroids by its excluded minors.
MSC:
| 05B35 | Combinatorial aspects of matroids and geometric lattices |
References:
| [1] | Bonin, J.; de Mier, A., Lattice path matroids: Structural properties, European J. Combin., 27, 701-738 (2006) · Zbl 1087.05014 |
| [2] | Bonin, J.; de Mier, A.; Noy, M., Lattice path matroids: Enumerative aspects and Tutte polynomials, J. Combin. Theory Ser. A, 104, 63-94 (2003) · Zbl 1031.05031 |
| [3] | Bonin, J.; Giménez, O., Multi-path matroids, Combin. Probab. Comput., 16, 193-217 (2007) · Zbl 1121.05023 |
| [4] | Brualdi, R. A., Transversal matroids, (White, N., Combinatorial Geometries (1987), Cambridge Univ. Press: Cambridge Univ. Press Cambridge), 72-97 · Zbl 0294.05018 |
| [5] | Crapo, H. H., Single-element extensions of matroids, J. Res. Nat. Bur. Standards Sect. B, 69B, 55-65 (1965) · Zbl 0141.21701 |
| [6] | de Mier, A., A natural family of flag matroids, SIAM J. Discrete Math., 21, 130-140 (2007) · Zbl 1147.05021 |
| [7] | de Mier, A.; Noy, M., A solution to the tennis ball problem, Theoret. Comput. Sci., 346, 254-264 (2005) · Zbl 1078.05006 |
| [8] | A. Gundert, E. Kim, D. Schymura, Lattice path and Lagrangian matroids (CRM report on research projects from the 2009 i-MATH Winter School DocCourse on Discrete and Computational Geometry).; A. Gundert, E. Kim, D. Schymura, Lattice path and Lagrangian matroids (CRM report on research projects from the 2009 i-MATH Winter School DocCourse on Discrete and Computational Geometry). |
| [9] | J. Lawrence, Some dual pairs of simple oriented matroids by concatenation, unpublished manuscript, 1984.; J. Lawrence, Some dual pairs of simple oriented matroids by concatenation, unpublished manuscript, 1984. |
| [10] | Oxley, J. G., Matroid Theory (1992), Oxford University Press: Oxford University Press Oxford · Zbl 0784.05002 |
| [11] | Oxley, J. G.; Prendergast, K.; Row, D., Matroids whose ground sets are domains of functions, J. Aust. Math. Soc. Ser. A, 32, 380-387 (1982) · Zbl 0485.05023 |
| [12] | V. Reiner, personal communication, 2008.; V. Reiner, personal communication, 2008. |
| [13] | Schweig, J., On the h-vector of a lattice path matroid, Electron. J. Combin., 17 (2010), Note 3, 6 pp · Zbl 1267.05057 |
| [14] | Stanley, R., Some combinatorial aspects of the Schubert calculus, (Combinatoire et Représentation du Groupe Dymétrique. Combinatoire et Représentation du Groupe Dymétrique, Lecture Notes in Math., vol. 579 (1977), Springer: Springer Berlin), 217-251 · Zbl 0359.05006 |
| [15] | Welsh, D. J.A., Matroid Theory (1976), Academic Press: Academic Press London · Zbl 0343.05002 |
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