Consider a graph whose nodes are the integer partitions of $n$, connected by an edge if you can get from one partition to the other by ‘sliding one square of its Young diagram’ – that is, if one partition can be gotten from the other by decrementing one of its values and either incrementing another value or adding a new value of 1.
I am interested in things like the degree distribution, mean degree, etc of this graph. Is anything known about this?