# Questions tagged [co.combinatorics]

Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.

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### Permutations of successive “jumps” in linear extensions

Given a poset $P$ on an $n$ element set $X$ if $L=(X,\leq)$ is a linear extenstion of $P$ then we index $\{x_1,\ldots x_n\}=X$ such that $x_1\leq \ldots \leq x_n$ - now if $C=(x_{i+1},\ldots x_{i+k})$ ...
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### Why do we not have a closed form expression for counting transitivity?

https://en.wikipedia.org/wiki/Transitive_relation. Are there any theoretical reasons out there which show us that why do we still not have a closed-form expression for transitivity counting. If you ...
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### Constructing set with maximal independent subset

What is the minimal $m$ such that there exists a set $A = \{a_1,...a_n\}$ of vectors : $a_i \in \{0,1\}^m$ ($n$ is given) such that every subset of vectors of size $k$ is independent, but only with ...
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### Logconcavity of height of Dyck paths

A finite sequence $a_i$ is called logconvace in case $a_i^2 \geq a_{i-1} a_{i+1}$. Question : For a fixed $n$, is the sequence $a_{n,k}$ giving the number of Dyck paths of semilength $n$ having ...
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### Distinct distances between adjacent equal elements

Let's call a sequence $a_1, \ldots, a_n$ suitable if for any positive integer $d$ there is at most one index $i$ such that $a_i = a_{i + d}$ and all elements $a_{i + 1}, \ldots, a_{i + d - 1}$ are not ...
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### Properties of sequences associated to Nakayama algebras

Assume Nakayama algebras are connected and given by quiver and relations. Note that such Nakayama algebras have global dimension at most $2n-2$ in case it is finite and the algebra has $n$ simples. ...
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### Terminology for transforming a directed acyclic graph into a tree

I am looking for the term of converting a directed acyclic graph (DAG) into a tree by traversing its topologically ordered nodes and copying the subtrees of the nodes with in-degree $> 1$. Such a ...
145 views

### Minimal generating set for $S_\omega$

If $G$ is a group and $S\subseteq G$, let $\langle S \rangle$ be the intersection of all subgroups of $G$ containing $S$. Let $S_\omega$ denote the group of all bijections $f:\omega\to\omega$ with ...
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### Algorithm for sampling stratification-constrained permutations

Let $\mathcal{X}$ be some base space, and let $\mathbf{S} =S_1, \ldots, S_N$ be a cover (not a partition, i.e. they can overlap) of $\mathcal{X}$. I will refer to the $S_i$ as strata, and to the cover ...
### Is the number of commutation classes of reduced words of the longest element of $S_n$ even for $n\geq 3$?
Observably, the number of primitive sorting networks on $n$ elements (or the number of commutation classes of reduced words of the longest element of $S_n$) is even for $3\leq n\leq 15$. These are all ...