The Number of 0-1-2 Increasing Trees as Two Different Evaluations of the Tutte Polynomial of a Complete Graph

@article{Merino2008TheNO,
  title={The Number of 0-1-2 Increasing Trees as Two Different Evaluations of the Tutte Polynomial of a Complete Graph},
  author={C. Merino},
  journal={Electr. J. Comb.},
  year={2008},
  volume={15}
}
If Tn(x, y) is the Tutte polynomial of the complete graph Kn, we have the equality Tn+1(1, 0) = Tn(2, 0). This has an almost trivial proof with the right combinatorial interpretation of Tn(1, 0) and Tn(2, 0). We present an algebraic proof of a result with the same flavour as the latter: Tn+2(1,−1) = Tn(2,−1), where Tn(1,−1) has the combinatorial interpretation of being the number of 0–1–2 increasing trees on n vertices. 

From This Paper

Topics from this paper.

Citations

Publications citing this paper.

References

Publications referenced by this paper.
Showing 1-10 of 10 references

Chip-firing and the Tutte polynomial

C. Merino
Annals of Combinatorics, • 1997
View 1 Excerpt

Counting colourings and flows in random graphs

D.J.A. Welsh
Janos Bolyai Math. Soc., Budapest, • 1996
View 1 Excerpt

The Tutte Polynomial and its Applications

T. Brylawski, J. Oxley
Matroid Applications. Cambridge University Press, Cambridge, • 1992

Rearrangements of the symmetric group and enumerative properties of the tangent and secant numbers

D. Foata, V. Strehl
Math. Z., • 1974

Groupes de réarrangements et nombres d’Euler

D. Foata
C. R. Acad. Sci. Paris Sr. A-B, 275, • 1972

Dévelopements de sec x et de tang x

D. André
C . R . Acad . Sc . Paris

G - parking functions and the Tutte polynomial

J. Plautz, R. Calderer
Preprint

Similar Papers

Loading similar papers…