Tutte polynomials of generalized parallel connections

Advances in Applied Mathematics

Volumn 32, Issue 1-2, 2004, Pages 31-43

  Bonin, Joseph ^a   de Mier, Anna ^b  

^a GEORGE WASHINGTON UNIVERSITY   (United States)

^b UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

Author keywords

Characteristics polynomial; Generalized parallel connection; k sum; Matroid; Tutte polynomial; Weighted characteristic polynomial

Indexed keywords

EID: 0345770550     PISSN: 01968858     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0196-8858(03)00076-9     Document Type: Article

References (14)

1. A. Andrzejak, Splitting formulas for Tutte polynomials, J. Combin. Theory Ser. B 70 (1997) 346-366.
2. J. Bonin, H. Qin, Tutte polynomials of q-cones, Discrete Math. 232 (2001) 95-103.
3. T. Brylawski, A combinatorial model for series-parallel networks, Trans. Amer. Math. Soc. 154 (1971) 1-22.
4. T. Brylawski, Modular constructions for combinatorial geometries, Trans. Amer. Math. Soc. 203 (1975) 1-44.
5. T. Brylawski, Intersection theory for embeddings of matroids into uniform geometries, Stud. Appl. Math. 61 (1979) 211-244.
6. T. Brylawski, The Tutte polynomial. I. General theory, in: A. Barlotti (Ed.), Matroid Theory and Its Applications, Liguori, Naples, 1982, pp. 125-175.
7. T. Brylawski, J.G. Oxley, The Tutte polynomials and its applications, in: N. White (Ed.), Matroid Applications, Cambridge Univ. Press, Cambridge, 1992, pp. 123-225.
8. H.H. Crapo, The Tutte polynomial, Aequationes Math. 3 (1969) 211-229.
9. E.G. Mphako, Tutte polynomials of perfect matroid designs, Combin. Probab. Comput. 9 (2000) 363-367.
10. J.G. Oxley, Matroid Theory, Oxford Univ. Press, Oxford, 1992.
11. G.-C. Rota, On the foundations of combinatorial theory. I. Theory of Möbius functions, Z. Wahrscheinlichkeits. Verw. Gebiete 2 (1964) 340-368.
12. P.D. Seymour, R.W. Weaver, A generalization of chordal graphs, J. Graph Theory 8 (1984) 241-251.
13. D.J.A. Welsh, Complexity: Knots, Colourings, and Counting, Cambridge Univ. Press, Cambridge, 1993.
14. T. Zaslavsky, The Möbius function and the characteristic polynomial, in: N. White (Ed.), Combinatorial Geometries, Cambridge Univ. Press, Cambridge, 1987, pp. 114-138.