Distributive Lattice Polyhedra

Yulia Kempner; Vadim E. Levit

doi:10.1016/j.endm.2009.07.080

Distributive Lattice Polyhedra

Yulia Kempner, Vadim E. Levit

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Poly-antimatroids are generalization of the notion of antimatroid to multisets. When the underlying set consists of only two elements, such two-dimensional poly-antimatroids correspond to point sets in the integer lattice Z^d. In this research we concentrate on geometrical properties of two-dimensional poly-antimatroids and prove that these sets form distributive lattice polyhedra. Our findings imply that two-dimensional poly-antimatroids have convex dimension 2. Further we investigate geometrical properties of three-dimensional distributive lattice polyhedra.

Original language	English
Pages (from-to)	483-487
Number of pages	5
Journal	Electronic Notes in Discrete Mathematics
Volume	34
DOIs	https://doi.org/10.1016/j.endm.2009.07.080
State	Published - 1 Aug 2009

Keywords

Antimatroid
convex dimension
distributive lattice
polyomino

Access to Document

10.1016/j.endm.2009.07.080

Cite this

@article{c1088b97e94f47c7af4ebfcddce5de82,

title = "Distributive Lattice Polyhedra",

abstract = "Poly-antimatroids are generalization of the notion of antimatroid to multisets. When the underlying set consists of only two elements, such two-dimensional poly-antimatroids correspond to point sets in the integer lattice Zd. In this research we concentrate on geometrical properties of two-dimensional poly-antimatroids and prove that these sets form distributive lattice polyhedra. Our findings imply that two-dimensional poly-antimatroids have convex dimension 2. Further we investigate geometrical properties of three-dimensional distributive lattice polyhedra.",

keywords = "Antimatroid, convex dimension, distributive lattice, polyomino",

author = "Yulia Kempner and Levit, \{Vadim E.\}",

year = "2009",

month = aug,

day = "1",

doi = "10.1016/j.endm.2009.07.080",

language = "אנגלית",

volume = "34",

pages = "483--487",

journal = "Electronic Notes in Discrete Mathematics",

issn = "1571-0653",

publisher = "Elsevier",

}

TY - JOUR

T1 - Distributive Lattice Polyhedra

AU - Kempner, Yulia

AU - Levit, Vadim E.

PY - 2009/8/1

Y1 - 2009/8/1

N2 - Poly-antimatroids are generalization of the notion of antimatroid to multisets. When the underlying set consists of only two elements, such two-dimensional poly-antimatroids correspond to point sets in the integer lattice Zd. In this research we concentrate on geometrical properties of two-dimensional poly-antimatroids and prove that these sets form distributive lattice polyhedra. Our findings imply that two-dimensional poly-antimatroids have convex dimension 2. Further we investigate geometrical properties of three-dimensional distributive lattice polyhedra.

AB - Poly-antimatroids are generalization of the notion of antimatroid to multisets. When the underlying set consists of only two elements, such two-dimensional poly-antimatroids correspond to point sets in the integer lattice Zd. In this research we concentrate on geometrical properties of two-dimensional poly-antimatroids and prove that these sets form distributive lattice polyhedra. Our findings imply that two-dimensional poly-antimatroids have convex dimension 2. Further we investigate geometrical properties of three-dimensional distributive lattice polyhedra.

KW - Antimatroid

KW - convex dimension

KW - distributive lattice

KW - polyomino

UR - https://www.scopus.com/pages/publications/67651154305

U2 - 10.1016/j.endm.2009.07.080

DO - 10.1016/j.endm.2009.07.080

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

AN - SCOPUS:67651154305

SN - 1571-0653

VL - 34

SP - 483

EP - 487

JO - Electronic Notes in Discrete Mathematics

JF - Electronic Notes in Discrete Mathematics

ER -

Distributive Lattice Polyhedra

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this