Abstract

Abstract The concept of with repetition was coined by Bjorner, Lovasz and Shor in 1991 as an extension of the notion of antimatroid in the framework of non-simple languages [Bjorner A., L. Lovasz, and P. R. Shor, Chip-firing games on graphs, European Journal of Combinatorics 12 (1991), 283–291]. There are some equivalent ways to define antimatroids. They may be separated into two categories: antimatroids defined as set systems and antimatroids defined as languages. For poly-antimatroids we use the set system approach. In this research we concentrate on interrelations between geometric, algorithmic, and lattice properties of poly-antimatroids. Much to our surprise it turned out that even the two-dimensional case is not trivial.

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