All Questions
10 questions
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votes
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57
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Reference for packing property and König property
Can someone please suggest reference material to study about the packing property and König property of ideals and some examples?
- 21
5
votes
1
answer
368
views
Six people standing on earth
Consider 6 people $p_i$, $i=1,\dots 6$, standing on a sphere $S^2$. We label the positions of these people by $p_i$ again. Suppose no pair of these points $p_i$ are antipodal. At each point $p_i$ ...
- 434
3
votes
0
answers
157
views
F-vectors of simplicial complex and f-vectors of non-faces of simplicial complex
Is there any result which gives us a relation between f-vector of simplicial complex and f-vector of nonfaces of a simplicial complex?
Thank you
- 51
2
votes
1
answer
196
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Circuit Reduction on Dual Graph of an Algebraic curve
I want to compute the resistance function r(p,q) between any two vertices of a fairly complicated graph. This resistance function is the one in Admissible pairing on a curve by Shouwu Zhang, section 3 ...
- 727
4
votes
0
answers
127
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Measuring the failure of basepoint independence of the rotor-routing model for non-planar ribbon graphs
In this question from 2012, Jordan Ellenberg asks if the set of spanning trees of a graph $G$ is naturally a torsor for the critical group (also called the sandpile group or the picard group $Pic^0(G)$...
5
votes
0
answers
230
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Minimal algebraic degree of symmetric unit distance embedding of Heawood graph
I'm looking at embeddings of the Heawood graph in the plane as unit distance graph. Apparently the first such embedding was given by Gerbracht, 2009 and has algebraic (over the rationals) coordinates ...
- 10.7k
18
votes
2
answers
700
views
Can all unit-distance graphs have their vertices at algebraic integers?
A graph $G$ is described as a unit-distance graph if there exists a function $f:G \rightarrow \mathbb{C}$ such that for every edge $(u,v) \in E(G)$, we have $|f(u) - f(v)| = 1$.
Obviously, we can ...
- 12.4k
0
votes
3
answers
622
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When does the rigidity matrix of a graph have full row rank?
Intuitive description: In the 2D plane, there are $m$ bars connected by $n$ joints. The length of each bar is fixed. These joints and bars can be viewed as a graph (see the figures below). Denote $s_i$...
- 61
51
votes
3
answers
4k
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What is the sandpile torsor?
Let G be a finite undirected connected graph. A divisor on G is an element of the free abelian group Div(G) on the vertices of G (or an integer-valued function on the vertices.) Summing over all ...
- 19.2k
8
votes
2
answers
692
views
Enumeration of graphs arising in invariant theory
I've been working on a talk based on some stuff in Olver's "Classical Invariant Theory" book and have been wondering about a related graph enumeration problem.
Start with a triple $(n,v,e)$ of ...
- 16k