Year: 2024
Type: preprint
Abstract: The volume of a cyclic polytope can be obtained by forming an iterated integral along a suitable piecewise linear path running through its edges. Different choices of such a path are related by the action of a subgroup of the combinatorial automorphisms of the polytope. Motivated by this observation, we look for other linear combinations of iterated integrals that are invariant under the subgroup action. This yields interesting polynomial attributes of the cyclic polytope. We prove that there are infinitely many of these invariants which are algebraically independent in the shuffle algebra.
Source: arXiv (Cornell University)
Authors: Lotter, Felix, Preiß, Rosa
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1875930355, G2117391915
OpenAlex ID: W4405469786