The number of 0-1-2 increasing trees as two different evaluations of the Tutte polynomial of a complete graph
Summary: If \(T_{n}(x,y)\) is the Tutte polynomial of the complete graph \(K_n\), we have the equality \(T_{n+1}(1,0)=T_{n}(2,0)\). This has an almost trivial proof with the right combinatorial interpretation of \(T_{n}(1,0)\) and \(T_{n}(2,0)\). We present an algebraic proof of a result with the same flavour as the latter: \(T_{n+2}(1,-1)=T_n(2,-1)\), where \(T_{n}(1,-1)\) has the combinatorial interpretation of being the number of 0--1--2 increasing trees on \(n\) vertices.
scientific article; zbMATH DE number 5540890