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

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

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 -