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arXiv · 0712.3996

On bases of tropical Plücker functions

Vladimir I. Danilov·Alexander V. Karzanov·Gleb A. Koshevoy
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Abstract

We consider functions $f:B\to\Rset$ that obey tropical analogs of classical Plücker 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 Plücker 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.

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Vladimir I. Danilov, Alexander V. Karzanov, Gleb A. Koshevoy. 2008-02-11. On bases of tropical Plücker functions. https://arxiv.org/abs/0712.3996

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