Syzygies on Tutte Polynomials of Freedom Matroids

作者：Kung Joseph P S^*

来源：Annals of Combinatorics, 2017, 21(4): 605-628.

DOI：10.1007/s00026-017-0370-0

• Tutte polynomial
• G-invariant
• freedom or nested matroids

It follows from a theorem of Derksen [J. Algebraic Combin., 30 (2009) 43-86] that the Tutte polynomial of a rank-r matroid on an n-set is "naturally" a linear combination of Tutte polynomials of rank-r size-n freedom matroids. However, the Tutte polynomials of rank-r size-n freedom matroids are not linearly independent. We construct two natural bases for these polynomials and as a corollary, we prove that the Tutte polynomials of rank-r matroids of size-n span a subspace of dimension . We also find a generating set for the linear relations between Tutte polynomials of freedom matroids. This generating set is indexed by a pair of intervals, one of size 2 and one of size 4, in the weak order of freedom matroids. This weak order is a distributive lattice and a sublattice of Young's partition lattice.

• 出版日期2017-12