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Apr
1
comment Absolutely algorithmically random infinite sequence
Isn't it the case that if we choose $f$ randomly (each value $f(n)$ independent, with probability 1/2 that $f(n)=0$), then the probability is 1 that $f$ is absolutely random?
Mar
30
answered Which graphs generate a matroidal independence complex?
Mar
29
comment Which graphs generate a matroidal independence complex?
It is not true that if $G$ is well-covered, then $I(G)$ is a uniform matroid. In fact, $I(G)$ need not be a matroid complex, e.g., the complement of a 4-vertex path.
Mar
22
revised Nonexistence of Limit Cycle
corrected spelling
Mar
19
awarded  Good Answer
Mar
18
awarded  Popular Question
Mar
16
asked Nonextendable partial Hadamard matrices
Mar
3
comment Why is the right permutohedron order (aka weak order) on $S_n$ a lattice?
@Darij, one way to prove this is by induction on $k-i$, the base case $k-i=2$ being clear. Is this enough of a hint?
Mar
2
comment Why is the right permutohedron order (aka weak order) on $S_n$ a lattice?
I don't have access to Berge's book now, but see the addendum to my answer.
Mar
2
revised Why is the right permutohedron order (aka weak order) on $S_n$ a lattice?
added 637 characters in body
Mar
1
answered Why is the right permutohedron order (aka weak order) on $S_n$ a lattice?
Feb
25
comment Number of subgroups of a given index of a free group
A more elegant way of stating Hall's result is $\log\sum_{d\geq 0} d!^{n-1} x^d= \sum_{d\geq 1}N(d,n)\frac{x^d}{d}$. See Enumerative Combinatorics, vol. 2, Exercise 5.13 for this and related results.
Feb
23
answered Number of matrices with no repeated columns or rows
Feb
22
comment Monotone mappings between finite partially ordered sets
This is the number $f(m,n) $ of order ideals of the product $C_m\times C_2^n$, where $C_i$ is an $i$-element chain. The number $g(n)$ of order ideals of $C_2^n$ is "Dedekind's problems," oeis.org/A000372. It is unlikely that there is a simple formula or even a fast way to compute $g(n)$, so probably also $f(m,n)$. The techniques used to estimate $g(n)$ can be applied to $f(m,n)$.
Feb
22
comment Groups of order $p(p^2+1)/2$
mathoverflow.net/questions/31553 (answer by R. Chapman) gives a characterization of those integers $n$ for which every finite group of order $n$ is abelian.
Feb
16
comment Why are some q-analogues more canonical than others?
One could add to Cigler's list the polynomials $\frac{[2]}{[2n+2]}{2n\brack n}$. They are essentially the characters of the principal specialization of a certain irreducible representation of the symplectic group Sp$(2n)$. Unlike $\frac{[1]}{[n+1]}{2n\brack n}$, they have unimodal coefficients.
Feb
14
asked A $q$-analogue of Foulkes' character related to alternating permutations
Feb
9
answered Number of solutions of linear homogenous Diophantine equation inside a box
Feb
9
answered Increasing tower of subsets of ${1, …, k}$
Feb
7
answered Permutation with restricted pairwise ordering