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WEAK TUTTE FUNCTIONS OF MATROIDS
"... Abstract. We find the universal module w(M) for functions (that need not be invariants) of finite matroids, defined on a minorclosed class M and with values in any module L over any commutative and unitary ring, that satisfy a parametrized deletioncontraction identity, F (M) = δeF (M � e) + γeF ( ..."
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F (M/e), when e is neither a loop nor a coloop. (F is called a (parametrized) weak Tutte function.) Within the universal module each matroid has a linear form t(M), its Tutte form, such that, for every weak Tutte function, F (M) is an evaluation of t(M) through a unique homomorphism w(M) → L. If L
Planning Algorithms
, 2004
"... This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning ..."
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Cited by 1108 (51 self)
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This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning under uncertainty, sensorbased planning, visibility, decisiontheoretic planning, game theory, information spaces, reinforcement learning, nonlinear systems, trajectory planning, nonholonomic planning, and kinodynamic planning.
Anticommutative Tutte Functions and Unimodular Oriented Matroids
, 2005
"... ... Tree and forest enumeration expressions for electrical resistance are generalized. We also demonstrate how the coranknullity polynomial, basis expansions with activities, and a geometric lattice expansion generalize to ported Tutte functions of oriented matroids. The ported Tutte functions are ..."
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... Tree and forest enumeration expressions for electrical resistance are generalized. We also demonstrate how the coranknullity polynomial, basis expansions with activities, and a geometric lattice expansion generalize to ported Tutte functions of oriented matroids. The ported Tutte functions
Lattice path matroids: enumerative aspects and Tutte polynomials
 J. COMBIN. THEORY SER. A
, 2003
"... Fix two lattice paths P and Q from (0, 0) to (m, r) that use East and North steps with P never going above Q. We show that the lattice paths that go from (0, 0) to (m, r) and that remain in the region bounded by P and Q can be identified with the bases of a particular type of transversal matroid, w ..."
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Cited by 33 (8 self)
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, which we call a lattice path matroid. We consider a variety of enumerative aspects of these matroids and we study three important matroid invariants, namely the Tutte polynomial and, for special types of lattice path matroids, the characteristic polynomial and the β invariant. In particular, we show
TUTTE POLYNOMIALS OF FLOWER GRAPHS
, 2009
"... We give explicit expressions of the Tutte polynomial of a complete flower graph and a flower graph with some petals missing. ..."
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Cited by 1 (0 self)
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We give explicit expressions of the Tutte polynomial of a complete flower graph and a flower graph with some petals missing.
Ported Tutte Functions of Extensors and Oriented Matroids
, 2006
"... The Tutte equations are ported (or setpointed) when the equations F(N) = geF(N/e) + reF(N \ e) are omitted for elements e in a distinguished set called ports. The solutions F, called ported Tutte functions, can distinguish different orientations of the same matroid. A ported extensor with ground se ..."
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The Tutte equations are ported (or setpointed) when the equations F(N) = geF(N/e) + reF(N \ e) are omitted for elements e in a distinguished set called ports. The solutions F, called ported Tutte functions, can distinguish different orientations of the same matroid. A ported extensor with ground
Splitting formulas for Tutte polynomials
, 1995
"... We present two splitting formulas for calculating the Tutte polynomial of a matroid. The first one is for a generalized parallel connection across a 3point line of two matroids and the second one is applicable to a 3sum of two matroids. An important tool used is the bipointed Tutte polynomial of a ..."
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Cited by 8 (0 self)
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We present two splitting formulas for calculating the Tutte polynomial of a matroid. The first one is for a generalized parallel connection across a 3point line of two matroids and the second one is applicable to a 3sum of two matroids. An important tool used is the bipointed Tutte polynomial
Results 1  10
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1,437