  The goal of this short paper to advertise the method of gauge transformations
(aka holographic reduction, reparametrization) that is well-known in
statistical physics and computer science, but less known in combinatorics. As
an application of it we give a new proof of a theorem of A. Schrijver asserting
that the number of Eulerian orientations of a $d$--regular graph on $n$
vertices with even $d$ is at least
$\left(\frac{\binom{d}{d/2}}{2^{d/2}}\right)^n$. We also show that a
$d$--regular graph with even $d$ has always at least as many Eulerian
orientations as $(d/2)$--regular subgraphs.
