Cyclic flats and corners of the linking polynomial
By:
References
- [1] D. Benard, A. Bouchet and A. Duchamp, On the Martin and Tutte polynomials, Technical Report, Département d’Informatique, Université du Maine, Le Mans, France, May 1997.
- [2] E. D. Bolker and H. Crapo, How to brace a one-story building, Environ. Plann. B Plann. Des., 4 (2) (1977), 125–152.
- [3] T. Brylawski, A combinatorial perspective on the Radon convexity theorem, Geom. Ded., 5 (1976), 459–466.
- [4] T. H. Brylawski, A decomposition for combinatorial geometries, Trans. Amer. Math. Soc. 171 (1972), 1–44.
- [5] T. H. Brylawski, The Tutte polynomial, part 1 : General theory. In A. Barlotti (ed). Matroid Theory and Its Applications, (C.I.M.E. 1980), Liguori, Naples, (1982), 125–275.
- [6] T. H. Brylawsky and J. Oxley, The Tutte polynomial and its applications, Matroid Application, N. L. White (Ed), Cambridge University Press, Cambridge, U.K, (1992), 123–225.
- [7] H. H. Crapo, The Tutte polynomial, Aeq. Math., 3 (1969), 211–229.
- [8] J. A. Ellis-Monaghan and I. Moffatt, The Las Vergnas polynomial for embedded graphs, Europ. J. Comb., 50 (2015), 97–114.
- [9] G. Etienne and M. Las Vergnas, External and internal elements of a matroid basis, Disc. Math., 179 (1998), 111–119.
- [10] K. K. Kayibi, S. Pirzada, On the p-bases of Matroid perspectives, Disc. Math., 339 (6) (2016), 1629–1639.
- [11] K. K. Kayibi, On the coefficients of the linking polynomial, Creative Mathematics and Informatics, 25 (2) (2016), 177–182.
- [12] W. Kook, V. Reiner and D. Stanton, A convolution formula for the Tutte polynomial, J. Comb. Theo. Ser. B, 76 (2) (1999), 297–300.
- [13] J. W. Leo, On coefficients of the Tutte polynomial, Disc. Math., 184 (1998), 121–125.
- [14] J. G. Oxley and G. Whittle, A characterization of Tutte invariants of2-polymatroids, J. Combin. Theory Ser. B59 (1993), 210–244.
- [15] J. G. Oxley and G. Whittle, Tutte invariants for 2-polymatroids, Contemporary Mathematics 147, Graph Structure Theory, (eds. N. Robertson and P. Seymour), (1995), pp. 9–20.
- [16] J. G. Oxley, Matroid Theory, Oxford University Press, New-York, (1992).
- [17] W. T. Tutte, A contribution to the theory of chromatic polynomials, Can. J. Math., 6 (1947), 80–91.
- [18] A. Recski, Maps of matroids with applications, Disc. Math., 303 (2005), 175–185.
- [19] M. Las Vergnas, The Tutte polynomial of a morphism of matroids I. setpointed matroids and matroid perspectives, Ann. Inst. Fourier, Grenoble, 49 (3) (1999), 973–1015.
- [20] M. Las Vergnas, On The Tutte polynomial of a morphism of matroids, Ann. Disc. Math, 8 (1980), 7–20.
- [21] M. Las Vergnas, Extensions normale d’un matroide, polynôme de Tutte d’un morphisme, C. R. Acad. Sci. Paris Sér A, 280 (1975), 1479–1482.
- [22] M. Las Vergnas, Acyclic and totally cyclic orientations of combinatorial geometries, Disc. Math., 20 (1977), 51–61.
- [23] M. Las Vergnas, Eulerian circuits of 4-valent graphs imbedded in surfaces, in L. Lovasz and V. Sos (eds), Algebraic Methods in Graph Theory, North-Holland, (1981) 451–478.
- [24] D. J. A. Welsh and K. K. Kayibi, A linking polynomial of two matroids, Adv. Appl. Math., 32 (2004), 391–419.
- [25] T. Zaslavsky, Facing up to arrangemens: face-count formulas for partitions of spaces by hyperplanes, Published by Mem. Amer. Math. Soc., Volume 1, Issue 1 154 (1975).
DOI: https://doi.org/10.2478/ausm-2018-0016 | Journal eISSN: 2066-7752
Language: English
Page range: 189 - 197
Submitted on: Dec 10, 2017
Published on: Sep 10, 2018
Published by: Sapientia Hungarian University of Transylvania
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year
Keywords:
Related subjects:
© 2018 Koko K. Kayibi, U. Samee, S. Pirzada, published by Sapientia Hungarian University of Transylvania
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.