Poly-antimatroid polyhedra

Yulia Kempner, Vadim E. Levit

פרסום מחקרי: פרסום בכתב עתמאמרביקורת עמיתים

תקציר

The notion of "antimatroid with repetition" was conceived by Bjorner, Lovasz and Shor in 1991 as an extension of the notion of antimatroid in the framework of non-simple languages. Further they were investigated by the name of "poly-antimatroids" (Nakamura, 2005, Kempner & Levit, 2007), where the set system approach was used. If the underlying set of a poly-antimatroid consists of n elements, then the poly-antimatroid may be representedas a subset of the integer lattice Zn. We concentrate on geometrical properties of two-dimensional (n = 2) poly-antimatroids - poly-antimatroid polygons, and prove that these polygons are parallelogram polyominoes. We also show that each two-dimensionalpoly-antimatroid is a poset poly-antimatroid, i.e., it is closed under intersection. The convex dimension cdim(S) of a poly-antimatroid S is the minimum number of maximal chains needed to realize S. While the convex dimension of an n-dimensionalpoly-antimatroid may be arbitrarily large, we prove that the convex dimension of an n-dimensional poset poly-antimatroid is equal to n.

שפה מקוריתאנגלית
עמודים (מ-עד)73-82
מספר עמודים10
כתב עתArs Mathematica Contemporanea
כרך7
מספר גיליון1
מזהי עצם דיגיטלי (DOIs)
סטטוס פרסוםפורסם - 2014

טביעת אצבע

להלן מוצגים תחומי המחקר של הפרסום 'Poly-antimatroid polyhedra'. יחד הם יוצרים טביעת אצבע ייחודית.

פורמט ציטוט ביבליוגרפי