Algebraic and Geometric Combinatorics on Lattice Polytopes

polymake and Lattice Polytopes

Discrete Mathematics & Theoretical Computer Science ◽

10.46298/dmtcs.2690 ◽

2009 ◽

Vol DMTCS Proceedings vol. AK,... (Proceedings) ◽

Cited By ~ 1

Author(s):

Michael Joswig ◽

Benjamin Müller ◽

Andreas Paffenholz

Keyword(s):

Convex Polytopes ◽

Software System ◽

Lattice Polytopes ◽

International Audience ◽

Geometric Combinatorics

International audience The $\mathtt{polymake}$ software system deals with convex polytopes and related objects from geometric combinatorics. This note reports on a new implementation of a subclass for lattice polytopes. The features displayed are enabled by recent changes to the $\mathtt{polymake}$ core, which will be discussed briefly.

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Polytopes and 𝐾-Theory

Georgian Mathematical Journal ◽

10.1515/gmj.2004.655 ◽

2004 ◽

Vol 11 (4) ◽

pp. 655-670

Author(s):

W. Bruns ◽

J. Gubeladze

Keyword(s):

Lattice Polytopes ◽

Unit Simplex

Abstract This is an overview of results from our experiment of merging two seemingly unrelated disciplines – higher algebraic 𝐾-theory of rings and the theory of lattice polytopes. The usual 𝐾-theory is the “theory of a unit simplex”. A conjecture is proposed on the structure of higher polyhedral 𝐾-groups for certain class of polytopes for which the coincidence of Quillen's and Volodin's theories is known.

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Enumeration of Hybrid Domino-Lozenge Tilings II: Quasi-Octagonal Regions

The Electronic Journal of Combinatorics ◽

10.37236/4669 ◽

2016 ◽

Vol 23 (2) ◽

Author(s):

Tri Lai

Keyword(s):

Product Formula ◽

Cambridge University ◽

Replacement Method ◽

Lozenge Tilings ◽

Simple Product ◽

Geometric Combinatorics

We use the subgraph replacement method to prove a simple product formula for the tilings of an 8-vertex counterpart of Propp's quasi-hexagons (Problem 16 in New Perspectives in Geometric Combinatorics, Cambridge University Press, 1999), called quasi-octagon.

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