A Tutte polynomial inequality for lattice path matroids
نویسندگان
چکیده
منابع مشابه
A Tutte polynomial inequality for lattice path matroids
Let M be a matroid without loops or coloops and let TM be its Tutte polynomial. In 1999 Merino and Welsh conjectured that max(TM (2, 0), TM (0, 2)) ≥ TM (1, 1) for graphic matroids. Ten years later, Conde and Merino proposed a multiplicative version of the conjecture which implies the original one. In this paper we show the validity of the multiplicative conjecture when M is a lattice path matr...
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Fix two lattice paths P and Q from ð0; 0Þ to ðm; rÞ that use East and North steps with P never going above Q: We show that the lattice paths that go from ð0; 0Þ to ðm; rÞ and that remain in the region bounded by P and Q can be identified with the bases of a particular type of transversal matroid, which we call a lattice path matroid. We consider a variety of enumerative aspects of these matroid...
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The complexity of computing the Tutte polynomial T(~/c,x,y) is determined for transversal matroid ,4s and algebraic numbers x and y. It is shown that for fixed x and y the problem of computing T(~,x,y) for JA a transversal matroid is ~pP-complete unless the numbers x and y satisfy (x 1)(y 1) = 1, in which case it is polynomial-time computable. In particular, the problem of counting bases in a t...
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ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 2018
ISSN: 0196-8858
DOI: 10.1016/j.aam.2016.11.008