7 papers
A formal framework for higher-order spin models via hypergraphs, polymatroids, and the Tutte polynomial
Khallil Berrekkal, Joanna A. Ellis-Monaghan, Merijn Moody +1
We develop a rigorous mathematical framework for statistical mechanics models on hypergraphs, and give conditions for lifting the classical connection between Potts model partition…
A Hypergraph Tutte Polynomial
Khallil Berrekkal, Joanna A. Ellis-Monaghan, Merijn Moody
We introduce a Tutte polynomial for hypergraphs, , together with , a related Tutte polynomial for -polymatroids. Both invariants admit deletion--contractio…
Polynomial invariants of cyclically ordered graphs
Paul Bratch, M. N. Ellingham, Joanna A. Ellis-Monaghan +2
Cyclically ordered graphs, or cogs, sit between abstract graphs and cellularly embedded graphs. They arise naturally in topological graph theory, knot theory, and mathematical biol…
Thistlethwaite Theorems for Knotoids and Linkoids
Sergei Chmutov, Qingying Deng, Joanna A. Ellis-Monaghan +2
The classical Thistlethwaite theorem for links can be phrased as asserting that the Kauffman bracket of a link can be obtained from an evaluation of the Bollobás-Riordan polynomia…
Maximum genus embeddings of dense eulerian graphs with specified faces
M. N. Ellingham, Joanna A. Ellis-Monaghan
We give a density condition for when, subject to a necessary parity condition, an eulerian graph or digraph may be cellularly embedded in an orientable surface so that it has exact…
A coarse Tutte polynomial for hypermaps
Joanna A. Ellis-Monaghan, Iain Moffatt, Steven Noble
We give an analogue of the Tutte polynomial for hypermaps. This polynomial can be defined as either a sum over subhypermaps, or recursively through deletion-contraction reductions…