All Questions
7 questions with no upvoted or accepted answers
9
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0
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205
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Reference for sparseness of incomparability graphs implying sparseness of covering graphs
If a partial order on $n$ elements has $m$ incomparable pairs, then its covering graph (aka Hasse diagram aka transitive reduction, the graph of pairs of elements that are comparable but are not the ...
- 18.6k
5
votes
0
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201
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Is this "trimming" of a supersolvable semimodular lattice known?
Let $L$ be a finite (upper) semimodular lattice. Recall that this means $L$ is graded and its rank function $\rho\colon L \to \mathbb{N}$ satisfies
$$ \rho(x) + \rho(y) \geq \rho(x\vee y)+\rho(x \...
- 24.2k
4
votes
0
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234
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To whom is the classification of atomic, modular finite lattices due?
Here lattice means a poset with meets and joins. A lattice is called atomic if every element is a join of atoms. There are a few different ways to define modular for finite lattices: one is that the ...
- 24.2k
3
votes
0
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95
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When is it possible to extend several linear orders defined "locally" into a single linear order defined "globally"?
This is a somewhat fuzzy question, so I will try my best to give a formulation which includes everything relevant while excluding everything else. I would like to find out if anyone else has studied ...
- 183
2
votes
0
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116
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Isomorphic subcategories of directed graphs and presets
For the purposes of this post, a digraph (directed graph) has neither loops nor multiple parallel edges, and a preset is an ordered pair consisting of a set $S$ and a preorder (viz., a reflexive and ...
- 10.5k
2
votes
0
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95
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A specific notion between the notions of transversal and system of distinct representatives.
Let $X$ be a set, let $\mathcal{C}$ be a collection of subsets of $X$, and let $x_1, \dots , x_k \in X$. Say that the sequence $\{x_i\}_{i=1\dots k}$ is a sequential transversal (of length $k$) ...
- 588
0
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0
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131
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terminology: monotone maps of posets such that the image of a lower set is a lower set
How are called in combinatorics
monotone maps of partially ordered sets such that the image of a lower set is a lower set, i.e. closed (or open) maps of finite topologies? Is there a classification ...
- 113