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1d

comment 
All relations among degree n monomials in n variables
You are asking for the first syzygy module of the $n$th Veronese subalgebra of $k[x_1,\dots,x_n]$. A relevant paper is arxiv.org/pdf/1403.4796.pdf. 
1d

awarded  Enlightened 
1d

awarded  Nice Answer 
1d

revised 
Expected size of determinant of $AA^T$ for nonsquare random $A$
new paragraph added 
1d

answered  Expected size of determinant of $AA^T$ for nonsquare random $A$ 
Jun 30 
comment 
Counting matrices of special types
@MaxAlekseyev I meant that you apply $(1,2)$ to both the rows and the columns. I see that you meant something else. 
Jun 30 
comment 
Counting matrices of special types
@MaxAlekseyev I don't think that your assertion about $k^{i\cdot j}$ is true. Let $k=2$, $\pi=\sigma=(1,2)$. Then the number of matrices invariant with respect to $\pi$ and $\sigma$ is four, not two. 
Jun 29 
comment 
Probability that random nonnegative integer matrix is singular
It has been conjectured that the probability that an $n\times n$ $\pm 1$ matrix $M$ is singular is asymptotic to the probability that two rows or columns of $M$ are equal up to sign (which is easy to compute). See users.uoa.gr/~apgiannop/matrices/Kahn_Komlos_Szemeredi_1995.pdf. Perhaps an analogue holds for matrices with entries $0,1,\dots,k$, e.g., two rows or columns being linearly dependent. 
Jun 27 
comment 
Is there a nice formula for the “noncrossing substitution” of linear combinatorial species?
Exercise 5.35 of Enumerative Combinatorics, vol. 2, is relevant. 
Jun 25 
awarded  Good Answer 
Jun 25 
comment 
Extrapolation between longest increasing and longest alternating subsequences
@TheMaskedAvenger: I have added the fact that $w=a_1\cdots a_n$. The case $f(n)>n$ is equivalent to $f(n)=n$. 
Jun 25 
revised 
Extrapolation between longest increasing and longest alternating subsequences
added "$w=$", "of $w$". 
Jun 25 
asked  Extrapolation between longest increasing and longest alternating subsequences 
Jun 24 
accepted  Combinatorial interpretation of ${i\choose n}$, where $i^2=1$ 
Jun 16 
awarded  Generalist 
Jun 15 
comment 
Finding the square root of a special matrix
If the entries of $A$ are $0,\pm x_i$ and $A$ is a symmetric matrix, then you are asking for a symmetric orthogonal design matrix. One reference is amazon.com/exec/obidos/ASIN/0824767748. 
Jun 15 
revised 
Evaluation of Macdonald Polynomials at $x_1=x_2=…=x_n = h$
"Macdonald" misspelled 
Jun 12 
comment 
Sum of irreducible complex character degrees for alternating groups
Following up on my previous comment, an interesting related result is that $\sum_\lambda f^\lambda (1)^{\frac 12(n\mathrm{rank}(\lambda))}$ equals the coefficient of $x^n/n!$ in $e^{x\frac{x^2}{2}}$. Here $\lambda$ ranges over all selfconjugate partitions of $n$, $f^\lambda$ is the dimension of the corresponding symmetric group character, and $\mathrm{rank}(\lambda)$ is size of the Durfee square of $\lambda$ (the largest $i$ for which $\lambda_i\geq i$). 
Jun 11 
answered  Representation numbers of numerical semigroups 
Jun 10 
awarded  Nice Answer 