论文信息 - Characterizations of PG(n - 1, q)\PG(k - 1, q) by Numerical and Polynomial Invariants

Characterizations of PG(n - 1, q)\PG(k - 1, q) by Numerical and Polynomial Invariants

We show that the simple matroid PG(n - 1, q)\PG(k - 1, q), for n > 4 and 1 ≤ k ≤ n - 2, is characterized by a variety of numerical and polynomial invariants. In particular, any matroid that has the same Tutte polynomial as PG(n - 1, q)\PG(k - 1, q) is isomorphic to PG(n - 1, q)\PG(k - 1, q).

Joseph E. Bonin | Rachelle M. Ankney | Rachelle M. Ankney

[1] William P. Miller,et al. Techniques in matroid reconstruction , 1997, Discret. Math..

[2] Joseph E. Bonin,et al. Characterizing Combinatorial Geometries by Numerical Invariants , 1999, Eur. J. Comb..

[3] P. Erdös. On an extremal problem in graph theory , 1970 .

[4] Tom Brylawski,et al. Intersection Theory for Embeddings of Matroids into Uniform Geometries , 1979 .

[5] H. Crapo,et al. The Tutte polynomial , 1969, 1707.03459.

[6] G. Rota,et al. On The Foundations of Combinatorial Theory: Combinatorial Geometries , 1970 .

[7] Tom Brylawski,et al. Matroid Applications: The Tutte Polynomial and Its Applications , 1992 .

[8] U. Faigle,et al. Book reviews , 1991, ZOR Methods Model. Oper. Res..

[9] Joseph E. Bonin. Matroids with No (q+2)-Point-Line Minors , 1996 .

[10] R. C. Bose,et al. A characterization of flat spaces in a finite geometry and the uniqueness of the hamming and the MacDonald codes , 1966 .

[11] Thomas H. Brylawski,et al. Hyperplane reconstruction of the Tutte polynomial of a geometric lattice , 1981, Discret. Math..