Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Mathematics > Combinatorics

arXiv:1809.08764 (math)
[Submitted on 24 Sep 2018]

Title:Graphical zonotopes with the same face vector

Authors:Zeying Xu
View PDF
Abstract:We are interested in constructing zonotopes which are combinatorially nonequivalent but have the same face vector. In this paper we introduce a quadrilateral flip operation on graphs. We show that, if one graph is obtained from another graph by a flip, then the face vectors of the graphical zonotopes of these two graphs are the same. In this way, we can easily construct a class of combinatorially nonequivalent graphical zonotopes which share the same face vector. It is known that all triangulations of the n-gon are connected through the flip operation. Thus their graphical zonotopes have the same face vector. We will compute this vector and the total number of faces.
Comments: 10 pages
Subjects: Combinatorics (math.CO)
MSC classes: 52B05
Cite as: arXiv:1809.08764 [math.CO]
  (or arXiv:1809.08764v1 [math.CO] for this version)
  https://doi.org/10.48550/arXiv.1809.08764

Submission history

From: Zeying Xu [view email]
[v1] Mon, 24 Sep 2018 05:08:46 UTC (23 KB)
Full-text links:

Access Paper:

  • View PDF
  • TeX Source
view license
Current browse context:
math.CO
< prev   |   next >
new | recent | 2018-09
Change to browse by:
math

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)