2022/11/21 by Eimear Byrne, Byrne, Eimear, Andrew Fulcher +1 · 1 citation
Mathematics · Computer Science · #Advanced Combinatorial Mathematics #Polynomial and algebraic computation #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2211.11666
We describe a construction of the Tutte polynomial for both matroids and q-matroids based on an appropriate partition of the underlying support lattice into intervals that correspond to prime-free minors, which we call a Tutte partition. We show that such partitions in the matroid case include the class of partitions arising in Crapo's definition of the Tutte polynomial, while not representing a direct q-analogue of such partitions. We propose axioms of q-Tutte-Grothendiek invariance and show that this yields a q-analogue of Tutte-Grothendiek invariance. We establish the connection between the rank polynomial and the Tutte polynomial, showing that one can be obtained from the other by convolution.