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      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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      1answer
      28 views

      Model for random graphs where clique number remains bounded

      In the Erd?s-Rényi model for random graphs,the clique number is seen to go to infinity al the number of vertices grows. Is anyone aware of models for random graphs with bounded ...
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      0answers
      65 views

      On the first sequence without collinear triple

      Let $u_n$ be the sequence lexicographically first among the sequences of nonnegative integers with graphs without collinear three points (as for $a_n=n^2$ or $b_n=2^n$). It is a variation of that one. ...
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      0answers
      42 views

      The scutoid as a noninscribable polyhedron

      I have no a good backround in combinatorial geometry but I would like to ask next question, because I think that it is interesting. I know from the book [1], section B18 and the post Combinatorially ...
      2
      votes
      1answer
      37 views

      Chromatic Polynomial when two disjoint graphs are joined at $2$ distinct points

      Consider a graph with chromatic polynomial $P(x)$ joined to a clique of order $k$ in two distinct points (joining here just means interesection of points). Then, what is the chromatic polynomial of ...
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      0answers
      48 views

      An upper bound on the minimum number of vertices in a girth 5 graph of chromatic number $k$

      Is there a known upper bound on the minimum number of vertices in a graph with girth 5 and chromatic number $k$? Could you also give references for this?
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      4answers
      436 views

      Sums of binomial coefficients weighted by incomplete gamma

      I am interested in proving that $$\sum_{k=0}^n\frac{k}{k!}\sum_{l=0}^{n-k}\frac{(-1)^l}{l!}=1 $$ and $$\sum_{k=0}^n\frac{k^2}{k!}\sum_{l=0}^{n-k}\frac{(-1)^l}{l!}=2. $$ I verified it numerically ...
      19
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      0answers
      424 views

      On the first sequence without triple in arithmetic progression

      In this Numberphile video (from 3:36 to 7:41), Neil Sloane explains an amazing sequence: It is the lexicographically first among the sequences of positive integers without triple in arithmetic ...
      9
      votes
      2answers
      342 views

      Regular subsets of $\text{PSL}(2, q)$

      Suppose a group $G$ acts on a set $\Omega$. Call a subset $A \subset G$ regular (or sharply transitive or simply transitive or...) if for every two points $\omega_1, \omega_2 \in \Omega$ there is a ...
      2
      votes
      1answer
      153 views

      What generalizes symmetric polynomials to other finite groups?

      Multivariate polynomial indexed by ${1, \ldots, n}$ are acted on by $S_n$: for $\sigma \in S_n$, define $\sigma(x_i) = x_{\sigma(x_i)}$, etc. Symmetric polynomials are those polynomials which are ...
      4
      votes
      0answers
      56 views

      Is there any edge- but not vertex-transitive polytope in $d\ge 4$ dimensions?

      I consider convex polytopes $P\subset\Bbb R^d$. The polytope is called vertex- resp. edge-transitive, if any vertex resp. edge can be mapped to any other by a symmetry of the polytope. I am looking ...
      1
      vote
      1answer
      33 views

      Induced subgraphs of the line graph of a dense linear hypergraph

      Given a hypergraph $H=(V,E)$ we associate to it its line graph $L(H)$ given by $V(L(H)) =E$ and $$E(L(H)) = \big\{\{e_1,e_2\}: e_1\neq e_2 \in E \text{ and } e_1\cap e_2 \neq \emptyset \big\}.$$ We ...
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      1answer
      42 views

      Rank and edges in a combinatorial graph?

      Fix a $d\in\mathbb N$ and consider the matrix $M\in\{0,1\}^{2^d\times d}$ of all $0/1$ vectors of length $d$. Consider the matrix $G\in\{0,1\}^{n\times n}$ whose $ij$ the entry is $0$ if inner product ...
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      0answers
      29 views

      Somewhat complicated Routing Problem [on hold]

      Based on routing problems, in this grid, how many ways can you go from A to B? What methods can be used here? Link to the Image
      2
      votes
      1answer
      111 views

      Combinatorial problem on periodic dyck paths from homological algebra

      edit: I added conjecture 2 that looks much more accessible. Here is the elementary combinatorial translation of the problem (read below for the homological background): Let $n \geq 2$. A Nakayama ...
      0
      votes
      1answer
      105 views

      From Steiner systems to geometric lattices to matroids

      I am looking for a specific matroid. I found a source that claimed to discuss these matroids, but then, only discusses geometric lattice. Even more, in that paper, the geometric lattice that seems to ...

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