bio | website | math.mit.edu/~rstan |
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location | ||
age | ||
visits | member for | 4 years, 5 months |
seen | 13 hours ago | |
stats | profile views | 8,515 |
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 |