On the theory of Pfaffian orientations. II: \(T\)-joins, \(k\)-cuts, and duality of enumeration
Associate a variable \(x_e\) with each edge of a graph \(G\). For each perfect matching \(P\) of a graph \(G\), let \(x(P)\) denote the product of the variables corresponding to the edges of \(P\). Let \({\mathcal P}(G,x)\) denote the polynomial which equals the sum of \(x(P)\) over all perfect matchings \(P\) of \(G\). In a similar way define \({\mathcal E}(G,x)\), \({\mathcal T}_T(G,x)\), and \({\mathcal C}_k(G,x)\) over the eulerian subgraphs, \(T\)-joins, and \(k\)-cuts of \(G\), respectively. The authors present a new combinatorial way to compute \({\mathcal T}_T(G,x)\) and \({\mathcal C}_k(G,x)\). They consider other polynomials and the weight enumerator of a binary code.
scientific article; zbMATH DE number 1247861