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The Merino-Welsh conjecture for split matroids. (English) Zbl 1526.05027

Summary: C. Merino and D. J. A. Welsh [ibid. 3, No. 2–4, 417–429 (1999; Zbl 0936.05043)] conjectured that evaluations of the Tutte polynomial of a graph satisfy an inequality. In this short article, we show that the conjecture generalized to matroids holds for the large class of all split matroids by exploiting the structure of their lattice of cyclic flats. This class of matroids strictly contains all paving and copaving matroids.

MSC:

05B35 Combinatorial aspects of matroids and geometric lattices
05C31 Graph polynomials
52B40 Matroids in convex geometry (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.)

Citations:

Zbl 0936.05043

Software:

SageMath
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Full Text: DOI arXiv

References:

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