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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.

        0
        votes
        0answers
        15 views

        Structure of color critical graph

        Let $G$ be a $k$-color critical graph on $N$ vertices. It is a known fact that every vertex of $G$ has at least $k-1$ neighbors (there are more results available on minimum number of edges in color ...
        -3
        votes
        0answers
        75 views

        Differential privacy [on hold]

        I'm reading the following book on privacy. https://www.cis.upenn.edu/~aaroth/Papers/privacybook.pdf however I'm having a lot of trouble making any kind of intuitive sense from the very complicated ...
        2
        votes
        2answers
        82 views

        Asymptotics of regular semisimple elements in finite groups of lie type

        Let $G$ be a reductive algebraic group defined over $\mathbb{F}_{q}$. Let $G(\mathbb{F_{q}})$ denote the finite group of fixed points under the Frobenius map $F$. Now, we know that the set of regular ...
        4
        votes
        0answers
        123 views

        Product of $q$-analogues

        Background Recall that the $q$-analogue $[n]_q\in\mathbb Z[q]$ of a natural number $n\in\mathbb N$ is defined as $$ [n]_q := \frac{q^n -1}{q-1}$$ the idea being that formulas involving $q$ will ...
        2
        votes
        1answer
        56 views

        Polynomial time decodable binary linear codes achieving $GV$ bound?

        Are there explicit or random construction of linear codes that achieve the $GV$ bound with polynomial time decodable property with alphabet size $q=2$? Tsfasman, Manin, Vladut beat the bound at ...
        4
        votes
        0answers
        77 views

        Generalized graph-minor theorem?

        Consider the following generalized graph-minor theorem: GM($κ,λ$): Given any collection $S$ of $κ$ simple undirected graphs each with less than $λ$ vertices, there are distinct graphs $G,H$ in $S$ ...
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        0answers
        80 views
        +500

        Does hereditary 2-coloring imply polychromatic 3-coloring for large edges?

        For a hypergraph $\mathcal H=(V,\mathcal E)$, denote by $m_k$ the smallest number for which we can $k$-color any $X\subset V$ such that for any $E\in \mathcal E$ with $|E\cap X|\ge m_k$ all $k$ colors ...
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        0answers
        119 views

        A binary wrap function [on hold]

        This question was inspired by a card puzzle. Define a wrap function to take an $N$-bit number to another $N$-bit number by "negating and reversing and wrapping leading bits" (this is just the ...
        9
        votes
        0answers
        97 views

        Irreducibility of root-height generating polynomial

        The height $ht(\alpha)$ of a positive root $\alpha$ in a (finite, crystallographic) root system $\Phi$ is $\sum_{i=1}^n c_i$ where $\alpha = \sum_{i=1}^n c_i \alpha_i$ is its decomposition as a sum of ...
        2
        votes
        1answer
        86 views

        Is there a two-dimensional Higman's lemma?

        A string over a finite alphabet $A$ can be thought of as a function $f:\{1,2,...,m\} \rightarrow A$ for some natural number $m$. A 2-Dim string over $A$ is a function $f$ where $f:\{1,2,\ldots,m\}\...
        0
        votes
        0answers
        80 views

        Kastanas' game and completely Ramsey sets

        recently I was reading the article ''On the Ramsey property for sets of reals'' of Ilias Kastanas (https://www.jstor.org/stable/2273667?seq=1#metadata_info_tab_contents), in this article the author ...
        7
        votes
        3answers
        322 views

        Arranging all permutations on $\{1,\ldots,n\}$ such that there are no common points

        If $n>0$ is an integer, let $[n]=\{1,\ldots,n\}$. Let $S_n$ denote the set of all permutations (bijections) $\pi:[n]\to[n]$. For which positive integers $n$ is there a bijection $\Phi:[n!]\to S_n$ ...
        1
        vote
        0answers
        27 views

        Minimum transitive dominating subtournament

        For any positive integer $k$, does there exist a tournament such that the smallest dominating set that forms a transitive subtournament has size exactly $k$? A tournament that does not work for $k>...
        4
        votes
        1answer
        45 views

        Calculate number of vertices adjacent to a clique, but not each other

        I have a network of N sensors and a test that tells me whether two sensor outputs are definitely not causally related. This allows me to construct a causality graph where each sensor is a vertex and ...
        0
        votes
        0answers
        16 views

        Difference between Adjacent strong edge coloring and vertex distinguishing strong edge coloring

        What is the exact difference between the adjacent strong edge coloring and vertex distinguishing proper edge coloring of graphs? This paper refers to the fact that the adjacent strong edge coloring of ...

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