Mathematics – Combinatorics
Scientific paper
2007-12-24
Mathematics
Combinatorics
44 pages. This is a revision of the original version, where some improvements are done and new results are added (in particula
Scientific paper
We consider functions $f:B\to\Rset$ that obey tropical analogs of classical Pl\"ucker relations on minors of a matrix. The most general set $B$ that we deal with in this paper is of the form $\{x\in \Zset^n\colon 0\le x\le a, m\le x_1+...+x_n\le m'\}$ (a rectangular integer box ``truncated from below and above''). We construct a basis for the set $\Tscr$ of tropical Pl\"ucker functions on $B$, a subset $\Bscr\subseteq B$ such that the restriction map $\Tscr\to\Rset^\Bscr$ is bijective. Also we characterize, in terms of the restriction to the basis, the classes of submodular, so-called skew-submodular, and discrete concave functions in $\Tscr$, discuss a tropical analogue of the Laurentness property, and present other results.
Danilov Vladimir I.
Karzanov Alexander V.
Koshevoy Gleb A.
No associations
LandOfFree
On bases of tropical Plücker functions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On bases of tropical Plücker functions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On bases of tropical Plücker functions will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-165506