TY - JOUR
T1 - A Geometric Characterization of Poly-antimatroids
AU - Kempner, Yulia
AU - Levit, Vadim E.
PY - 2007/3/1
Y1 - 2007/3/1
N2 - The concept of "antimatroid 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 [Björner A., L. Lovász, 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.
AB - The concept of "antimatroid 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 [Björner A., L. Lovász, 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.
KW - Abstract convexity
KW - multiset
KW - poly-antimatroid
UR - http://www.scopus.com/inward/record.url?scp=33847309642&partnerID=8YFLogxK
U2 - 10.1016/j.endm.2007.01.050
DO - 10.1016/j.endm.2007.01.050
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AN - SCOPUS:33847309642
SN - 1571-0653
VL - 28
SP - 357
EP - 364
JO - Electronic Notes in Discrete Mathematics
JF - Electronic Notes in Discrete Mathematics
ER -