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Results tagged with posets
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user 33089
A poset or partially ordered set is a set endowed with a partial order, meaning a binary relation $\leq$ which is reflexive ($x \leq x$ for all $x$), antisymmetric ($x\leq y$ and $y\leq x$ implies $x=y$), and transitive ($x\leq y$ and $y\leq z$ implies $x \leq z$).
1
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$r$-differential posets: current state of the art
I have a recent paper in which I prove that when $r=1$ or $r$ is prime, $Y^r$ is the only $r$-differential poset (or more generally $r$-dual graded graph) which comes from the branching rules for some …
- 2,743
2
votes
Examples of differential towers of groups
After thinking about the problem for a while, I recently posted this paper which answers this question when $r$ is one or prime. I show:
Theorem: If $r$ is one or prime, then, even without requiring …
- 2,743
5
votes
Accepted
Linear Extension of the $n\times n$ lattice
The $n \times n$ lattice just means the product poset of two chains: $[0,n] \times [0,n]=\{(i,j) | 0 \leq i,j \leq n\}$ where $(i,j) \leq (i',j')$ if and only if $i \leq i'$ and $j \leq j'$.
A linear …
- 2,743
10
votes
1
answer
198
views
Examples of differential towers of groups
This is a restatement of the fact that Young's lattice $Y$ and its powers $Y^r$ are $(r$-)differential posets.
Are there any other known examples of differential towers of groups? …
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