The 2-factor polynomial detects even perfect matchings (Q2185217)

2-factor polynomials of a plane cubic graph \(G\) equipped with a perfect matching \(M\) were introduced by developing their cohomology theory as the graded Euler characteristic, which is also the 2-factor bracket of a perfect matching drawing for the pair \((G,M)\) as the Laurent polynomial in the variable \(z\) (see [\textit{S. Baldridge}, ``A cohomology theory for planar trivalent graphs with perfect matchings'', Preprint, \url{arXiv:1810.07302}]). This paper under review proves that the value of the 2-factor polynomial of \((G,M)\) at \(z=1\) equals the number of 2-factors of \(G\) containing the perfect matching \(M\), which thus conforms Conjecture 1.2 proposed by Baldridge [loc. cit.]. This result also implies that if this value is positive, then \(M\) is an even perfect matching.