Abstract: Crapo's beta invariant was defined by Henry Crapo in the 1960s. For a matroid M, the invariant β(M) is the non-negative integer that is the coefficient of the x term of the Tutte polynomial. Crapo proved that β(M) is greater than 0 if and only if M is connected and M is not a loop, and Brylawski proved that M is the matroid of a series-parallel network if and only if M is a co-loop or β(M)=1. In this talk, we present several generalizations of the beta invariant to combinatorial structures that are not matroids. We concentrate on posets, chordal graphs, and finite subsets of Euclidean space. In each case, our definition of β measures the number of "interior'' elements.
Recording during the meeting "Combinatorial Geometries: Matroids, Oriented Matroids and Applications" the September 27, 2018 at the Centre International de Rencontres Mathématiques (Marseille, France)
Filmmaker: Guillaume Hennenfent
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities:
- Chapter markers and keywords to watch the parts of your choice in the video
- Videos enriched with abstracts, bibliographies, Mathematics Subject Classification
- Multi-criteria search by author, title, tags, mathematical area
Recording during the meeting "Combinatorial Geometries: Matroids, Oriented Matroids and Applications" the September 27, 2018 at the Centre International de Rencontres Mathématiques (Marseille, France)
Filmmaker: Guillaume Hennenfent
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities:
- Chapter markers and keywords to watch the parts of your choice in the video
- Videos enriched with abstracts, bibliographies, Mathematics Subject Classification
- Multi-criteria search by author, title, tags, mathematical area
Gary Gordon and Liz McMahon: Generalizations of Crapo's Beta Invariant cnrs montpellier | |
2 Likes | 2 Dislikes |
57 views views | 10K followers |
Science & Technology | Upload TimePublished on 19 Oct 2018 |
Không có nhận xét nào:
Đăng nhận xét