TITLE: Partial order relation on subsets
QUESTION [9 upvotes]: 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

REPLY [6 votes]: This order is sometimes denoted $L(k,n-k)$ and has many interesting properties. See for instance Chapter 6 of http://math.mit.edu/~rstan/algcomb.pdf. For the characteristic polynomial of the Hasse diagram of $L(k,n-k)$ (considered as a graph), see Remark 5.6 of http://math.mit.edu/~rstan/papers/vac.pdf.