An improved lower bound for the maximal length of a multivector

TL;DR

This paper introduces a significantly improved lower bound for the maximal length of multivectors, revealing that their length grows polynomially with the dimension, which has important implications for quantum chemistry.

Contribution

It presents a new lower bound that is closer to the upper bound, showing polynomial growth and challenging previous estimates of multivector length.

Findings

New lower bound is closer to the upper bound.

Maximal length grows polynomially with dimension.

Implications for quantum chemistry applications.

Abstract

A new lower bound for the maximal length of a multivector is obtained. It is much closer to the best known upper bound than previously reported lower bound estimates. The maximal length appears to be unexpectedly large for $n$-vectors, with n>2, since the few exactly known values seem to grow linearly with vector space dimension, whereas the new lower bound has a polynomial order equal to n-1 like the best known upper bound. This result has implications for quantum chemistry.