Tagged Questions

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Abbreviations in Combinatorial Graph/Matrix theory

I'm getting started with research in combinatorics. I have come across a reference that uses a great deal of abbreviations. I was able to figure most of them out but there are a few that I can find. ...
178 views

Extending a partial order to antichains

Let $(S, \leq)$ be a partial order. Let $T$ be the set of antichains of $S$ (i.e., subsets of $S$ whose elements are pairwise incomparable). Define a relation $\leq'$ on $T$ as follows: for all $A$, ...
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What are the sets of vertices in a proper vertex coloring referred to?

A (proper) vertex coloring of a graph is a labelling of the graph’s vertices with colors such that no two vertices sharing the same edge have the same color. A coloring using at most $k$ colors is ...
919 views

Meaning of counting argument?

Does "counting argument" mean a proof of some statements by counting something? Is "counting argument" same as "double counting"? Or does it include both double counting and bijective proof? I ...
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Combination of n sets that produces a set of n-tuple

Given n sets with 3 elements: $X_i=\{a_i,b_i,c_i\}$ where $\{i\in\mathbb{N}|1\leq i\leq n\}$. How can I define a n-tuple based on combination of this sets that produces the set $S$ with $3^n$ ...
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Is there a word to describe the set of permutations of each member of the powerset of a set?

Just what it says on the tin: For a set, X, is there a word to describe the union of sets of permutations of each member of the powerset of X?
286 views

What are k-cycles?

I came across the following question:If we pick a random permutation of $n$ distinct letters,what is the probability that our permutation has at most $k$ cycles? I am not sure I understand the ...
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simplex and power set

I read the following: Let $M$ be a set. The simplex on $M$ is the set of all subsets of $M$; we denote this by $\Delta_M$. We will sometimes refer to the elements of $M$ as vertices of $\Delta_M$. A ...
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The polynomial where only the terms in the multinomial series where each variable's exponent is $>0$ are kept?

I'm wondering if there's a special polynomial with a name out there with $x_1,x_2,\ldots,x_k$ as variables that's defined like this:  \sum_{\substack{i_1>0,i_2>0, \ldots,i_k>0 \\ i_1 ...
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Is there are a name for a simplicial complex that is homotopic to the clique complex of its 1-skeleton?

A hollow octahedron is a nice triangulation of the sphere, because once you know the edges, you know everything. The vertices are obviously the ends of the edges, and the faces are any collection of ...
516 views

How to pronounce “tableaux”?

How do you pronounce Young tableaux? Does it sound just like its singular form?
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Does this generalisation of Latin squares have a name?

I am interested in looking at $n\times n$ tableaux (or matrices) in which (WLOG) each integer in $\{ 1, 2, \ldots, n \}$ occurs exactly $n$ times. This is a generalisation of a Latin (or even ...