TY - JOUR
T1 - Geometry of poset antimatroids
AU - Kempner, Yulia
AU - Levit, Vadim E.
PY - 2013/5/15
Y1 - 2013/5/15
N2 - An antimatroid is an accessible set system closed under union. A poset antimatroid is a particular case of antimatroid, which is formed by the lower sets of a poset. Feasible sets in a poset antimatroid ordered by inclusion form a distributive lattice, and every distributive lattice can be formed in this way. We introduce the polydimension of an antimatroid as the minimum dimension d such that the antimatroid may be isometrically embedded into d-dimensional integer lattice Zd. We prove that every antimatroid of poly-dimension 2 is a poset antimatroid, and demonstrate both graph and geometric characterizations of such antimatroids. Finally, a conjecture concerning poset antimatroids of arbitrary poly-dimension d is presented.
AB - An antimatroid is an accessible set system closed under union. A poset antimatroid is a particular case of antimatroid, which is formed by the lower sets of a poset. Feasible sets in a poset antimatroid ordered by inclusion form a distributive lattice, and every distributive lattice can be formed in this way. We introduce the polydimension of an antimatroid as the minimum dimension d such that the antimatroid may be isometrically embedded into d-dimensional integer lattice Zd. We prove that every antimatroid of poly-dimension 2 is a poset antimatroid, and demonstrate both graph and geometric characterizations of such antimatroids. Finally, a conjecture concerning poset antimatroids of arbitrary poly-dimension d is presented.
KW - Antimatroid
KW - Dimension
KW - Poset antimatroid
UR - http://www.scopus.com/inward/record.url?scp=84878156860&partnerID=8YFLogxK
U2 - 10.1016/j.endm.2013.05.031
DO - 10.1016/j.endm.2013.05.031
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AN - SCOPUS:84878156860
SN - 1571-0653
VL - 40
SP - 169
EP - 173
JO - Electronic Notes in Discrete Mathematics
JF - Electronic Notes in Discrete Mathematics
ER -