Proceedings of the 28-th International Conference on Formal Power Series and Algebraic Combinatorics
4-8 Jul 2016 Vancouver, British Columbia (Canada)

Extended abstracts listed by author > Traldi Lorenzo

Fourientation activities and the Tutte polynomial: Extended abstract
Spencer Backman  1  , Sam Hopkins  2  , Lorenzo Traldi  3  
1 : Hausdorff Center for Mathematics  (HCM)  -  Website
Hausdorff Center for Mathematics Villa Maria Endenicher Allee 62 D-53115 Bonn Germany -  Allemagne
2 : Department of Mathematics [MIT]  -  Website
Headquarters Office Building 2, Room 236 77 Massachusetts Avenue Cambridge, MA 02139-4307 -  États-Unis
3 : Lafayette College [Easton]  -  Website
730 High St, Easton, PA 18042 -  États-Unis

A fourientation of a graph G is a choice for each edge of the graph whether to orient that edge in either direction, leave it unoriented, or biorient it. We may naturally view fourientations as a mixture of subgraphs and graph orientations where unoriented and bioriented edges play the role of absent and present subgraph edges, respectively. Building on work of Backman and Hopkins (2015), we show that given a linear order and a reference orientation of the edge set, one can define activities for fourientations of G which allow for a new 12 variable expansion of the Tutte polynomial TG. Our formula specializes to both an orientation activities expansion of TG due to Las Vergnas (1984) and a generalized activities expansion of TG due to Gordon and Traldi (1990). 

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