<em id="zlul0"></em><dl id="zlul0"><menu id="zlul0"></menu></dl>

    <em id="zlul0"></em>

      <dl id="zlul0"></dl>
        <div id="zlul0"><tr id="zlul0"><object id="zlul0"></object></tr></div>
        <em id="zlul0"></em>

        <div id="zlul0"><ol id="zlul0"></ol></div>

        Stack Exchange Network

        Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

        Visit Stack Exchange

        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
        10 views

        Making a not-multi graph from a multigraph

        Given $k$ girls, they are given $kn$ balls so that each girls has $n$ balls. Balls are coloured with $n$ colours so that there are $k$ balls of each color. Two girls may exchange the balls (1 ball for ...
        2
        votes
        0answers
        43 views

        Can one enumerate the set partitions of the faces of a regular dodecahedron mathematically?

        If we partition the faces of a regular dodecahedron into one nonempty subset, there is only one partition; for twelve nonempty subsets, there is also just one partition; for eleven nonempty subsets ...
        2
        votes
        0answers
        75 views

        On covers of groups by cosets

        Suppose that ${\cal A}=\{a_sG_s\}_{s=1}^k$ is a cover of a group $G$ by (finitely many) left cosets with $a_tG_t$ irredundant (where $1\le t\le k$). Then the index $[G:G_t]$ is known to be finite. In ...
        0
        votes
        0answers
        71 views

        Arithmetic that corresponds to combinatorial rectangles and cylinder intersections?

        Definable subsets of $\mathbb N$ in the language of Presburger arithmetic are exactly the eventually periodic sets. In communication complexity the interpretation is more on intersection and union of ...
        3
        votes
        1answer
        121 views

        Generating function for lattice paths making aribitrary (i,j)-up-right move in one step and fitting rectangular (m,n)?

        There is the following beautiful formula (see Qiaochu Yuan excellent blog): $$ \sum_{\lambda \in Young~diagrams~fitting~rectangle~m~n} q^{Box~count(="area~under~the~curve")~of~\lambda} = \binom{n+m}{...
        0
        votes
        0answers
        51 views

        Find large “induced” bipartite graph in a dense graph?

        Do there exist constants $d>0$, $0<c<1$, $\delta>0$ so that for all large $n$, there exists a graph $H$ satisfying $$e_H\ge dn^2,$$ and then no matter how we remove some edges from $H$ to ...
        7
        votes
        1answer
        103 views

        Formula for number of permutations less than a given permutation in weak order

        Let $w\in S_n$ be a permutation. Is there a reasonable "formula" for the number of elements of the initial interval $[e,w]$ of weak (Bruhat) order from the identity to $w$? In terms of what such a "...
        1
        vote
        1answer
        72 views

        Matrix of powers of pairwise differences

        Let $\underline{c}:=\left(c_1,\dots,c_n\right)$ be pairwise distinct complex numbers, and let $k$ be a non-negative integer. Define the matrix $A_{n,k}(\underline{c})$ to contain the $k$-th powers of ...
        2
        votes
        0answers
        86 views

        Proving that $\lambda\mapsto \chi^\lambda(C)/f^\lambda$ is a polynomial

        Let $\lambda$ be a partition of $n$ and $\chi^\lambda$ be the character of $S_n$ associated to it. Given any conjugacy class $C$, I want to prove that $$\lambda\mapsto \frac{\chi^\lambda(C)}{f^\lambda}...
        -2
        votes
        0answers
        40 views

        Combinatorics - Maximum No. of ways to visit all the cities in list starting from 1st city [on hold]

        You are given a list consisting of only 1's and 0's, if the value of given element is 1 then you can travel to any city such that 1<= |i-j|<=2 , where i is the position of current city and j is ...
        0
        votes
        0answers
        16 views

        How to infer the number of subsequences of array equal with the number all combination of array? [on hold]

        If I have an array of size n. I want the number of all subsequences of it (contains empty). For example: [1, 2, 3] 's all ...
        0
        votes
        0answers
        105 views

        A binomial coefficient identity

        i'm unable to prove the following : $\forall n$ integer $\geq 3$, $ \displaystyle \displaystyle \sum_{s=1}^n \sum_{j=n-s+1}^n \displaystyle \frac{ (\binom n j )^2 \binom {n+j} n }{s-n+j} ( \...
        4
        votes
        0answers
        48 views

        Large finite subsets of Euclidean space with no isosceles (or approximately isosceles) triangles

        Here's a question in combinatorial geometry which feels very much like other questions I'm familiar with but which I can't see how to get a hold of. I'll actually propose two different questions on ...
        2
        votes
        1answer
        81 views

        Maximum number of $0$-$1$ vectors with a given rank

        Let $k\ge2$. The maximum number of $0$-$1$ (column) vectors of length $2k-1$ which make a rank $k$ matrix with no zero row nor two identical rows is $2^{k-1}+1$. (The rank is over the rationals.) I ...
        2
        votes
        1answer
        109 views

        “Oddity” of $q$-Catalan polynomials: Part II

        This question extends my earlier MO post for which I'm grateful for answers and useful comments. The Catalan numbers $C_n=\frac1{n+1}\binom{2n}n$ satisfy: $\text{$C_{1,n}$ is odd iff $n=2^j-1$ for ...

        15 30 50 per page
        山西福彩快乐十分钟
          <em id="zlul0"></em><dl id="zlul0"><menu id="zlul0"></menu></dl>

          <em id="zlul0"></em>

            <dl id="zlul0"></dl>
              <div id="zlul0"><tr id="zlul0"><object id="zlul0"></object></tr></div>
              <em id="zlul0"></em>

              <div id="zlul0"><ol id="zlul0"></ol></div>
                <em id="zlul0"></em><dl id="zlul0"><menu id="zlul0"></menu></dl>

                <em id="zlul0"></em>

                  <dl id="zlul0"></dl>
                    <div id="zlul0"><tr id="zlul0"><object id="zlul0"></object></tr></div>
                    <em id="zlul0"></em>

                    <div id="zlul0"><ol id="zlul0"></ol></div>