Poslední úprava: doc. Mgr. Jan Kynčl, Ph.D. (05.05.2019)
In this course for advanced undergraduates and graduates given by Fulbright-Charles University Distinguished
Chair Prof. Ellis-Monaghan, the Tutte polynomial is used to showcase a variety of principles and techniques for
other graph polynomials and related topological invariants. Applications include statistical physics, knot theory and
DNA sequencing.
Poslední úprava: doc. Mgr. Jan Kynčl, Ph.D. (05.05.2019)
In this course for advanced undergraduates and graduates given by Fulbright-Charles University Distinguished
Chair Prof. Ellis-Monaghan, the Tutte polynomial is used to showcase a variety of principles and techniques for
other graph polynomials and related topological invariants. Applications include statistical physics, knot theory and
DNA sequencing.
Literatura -
Poslední úprava: doc. Mgr. Jan Kynčl, Ph.D. (04.05.2019)
J. Ellis-Monaghan, C. Merino, Graph polynomials and their applications I: the Tutte polynomial, in Structural Analysis of Complex Networks, Matthias Dehmer, ed., Birkhauser, 2010.
J. Ellis-Monaghan, C. Merino, Graph polynomials and their applications II: interrelations and interpretations, in for Structural Analysis of Complex Networks, Matthias Dehmer, ed., Birkhauser, 2010.
Poslední úprava: doc. Mgr. Jan Kynčl, Ph.D. (04.05.2019)
J. Ellis-Monaghan, C. Merino, Graph polynomials and their applications I: the Tutte polynomial, in Structural Analysis of Complex Networks, Matthias Dehmer, ed., Birkhauser, 2010.
J. Ellis-Monaghan, C. Merino, Graph polynomials and their applications II: interrelations and interpretations, in for Structural Analysis of Complex Networks, Matthias Dehmer, ed., Birkhauser, 2010.
Sylabus -
Poslední úprava: doc. Mgr. Jan Kynčl, Ph.D. (04.05.2019)
The Tutte polynomial. Several definitions and universality.
Evaluations and specializations of the Tutte polynomial.
Multivariable and topological generalizations of the Tutte polynomial
Applications of the Tutte polynomial
Transition, Martin, and Penrose polynomials.
The generalized transition polynomial with multivariable and topological extensions.
The interlace polynomial
Applications to DNA sequencing and DNA self-assembly.
Connections with knot theory.
Independence, characteristic, and matching polynomials.
Poslední úprava: doc. Mgr. Jan Kynčl, Ph.D. (04.05.2019)
The Tutte polynomial. Several definitions and universality.
Evaluations and specializations of the Tutte polynomial.
Multivariable and topological generalizations of the Tutte polynomial
Applications of the Tutte polynomial
Transition, Martin, and Penrose polynomials.
The generalized transition polynomial with multivariable and topological extensions.
The interlace polynomial
Applications to DNA sequencing and DNA self-assembly.
Connections with knot theory.
Independence, characteristic, and matching polynomials.