Generalized polynomial invariants for virtual knots via parity

By extending the quiver state model that calculates the generalized Alexander polynomial defined by Kauffman and Radford, we introduce a new state model via the parity for crossings and define a polynomial called the even generalized Alexander polynomial in the paper. We prove that this polynomial is an invariant of virtual knots and show that there is a specific virtual knot that can be distinguished from the trivial knot by the polynomial. We introduce other generalized polynomial invariants via parity.