 Lefschetz coincidence number

For maps $f,g:M\to N$ between closed connected oriented manifolds of equal dimension, the rational Lefschetz coincidence number is the displayed alternating trace, using the cohomological pushforward between closed oriented manifolds. Equivalently it evaluates the pullback by $(f,g)$ of the cohomology class of the diagonal on $[M]$. This formula fixes the signs with the product orientation on $N\times N$.