I'm looking for a reference for the statement that almost every partial order on $n$ elements has trivial automorphism group. I've been told that this is a folklore result. Does anyone know of a good reference?



Reference for statement that almost every $n$-element partial order has trivial automorphism group
Prömel (1987) proves a more general statement of rigidity for many classes of structures. In particular he has:


Corollary 2.3. Let $P^u(n)$ denote the number of unlabeled partial orders
on an $n$-element set. Then there exists a constant $s$ such that for all $n$
$$
P^u(n) \le \frac{P(n)}{n!} \left(1 + \frac{s}{2^{n/4}} \right),
$$


and as a consequence,


Corollary 2.3.a. Almost all partial orders are rigid, i.e., have no non-trivial automorphism.


*Prömel, Hans Jürgen*, [**Counting unlabeled structures**](http://dx.doi.org/10.1016/0097-3165(87)90061-6), J. Comb. Theory, Ser. A 44, 83-93 (1987). [ZBL0618.05029](https://zbmath.org/?q=an:0618.05029).


