Totally symmetric functions are reconstructible from identification minors

The Electronic Journal of Combinatorics, 21(2) (2014), #P2.6
http://www.combinatorics.org/ojs/index.php/eljc/article/view/v21i2p6

We formulate a reconstruction problem for functions of several arguments: Is a function of several arguments uniquely determined, up to equivalence, by its identification minors? We establish some positive and negative results on this reconstruction problem. In particular, we show that totally symmetric functions (of sufficiently large arity) are reconstructible.