I consider all $k$ element subsets of the set $\{1,\ldots,n\}$ and define a partial order relation $\prec$ as follows: $\{a_1,\ldots,a_k\}\prec\{b_1,\ldots,b_k\}$, if and only if $a_1<\cdots<a_k$, $b_1<\cdots<b_k$ and $a_i\leq b_i$ for all $i=1,\ldots,k$.

What is this partial order commonly called in the literature? Can someone point out references?

Thanks a lot, Torsten

[edit] Here is a Hasse diagram of this partial order for $n=6$ and $k=3$: http://www.freeimagehosting.net/7pmk7