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21h
comment An (open?) problem about a sequence of nested principal sub-matrices and their determinants
For a positive definite matrix, every principal minor is positive.
Apr
16
answered Young tableau with no i in row i, name that derangement
Apr
14
awarded  Necromancer
Apr
14
awarded  Good Answer
Apr
6
answered Finite distributive lattices not contained in $\omega^\omega$
Apr
5
comment Existence of a “quasi-uniform” probablility distribution on $\mathbb{Z}$
I'm not sure why this is downvoted. Though I am making the standard assumption that probability distributions are countably additive, it still makes sense to ask my question for finitely additive probability distributions. See for instance math.stackexchange.com/questions/203220/….
Apr
3
comment Polytopes whose intersections have few vertices
An intersection of two simplices in $\mathbb{R}^n$ has at most $2n+2$ facets. By the Upper Bound Theorem for polytopes, the number of vertices is at most $2\sum_{i=0}^{(n-1)/2}{n+i+1\choose i}$ if $n$ is odd, and $2\sum_{i=0}^{\frac n2-1}{n+i+1\choose i} + {\frac{3n}{2}+1\choose \frac n2}$ if $n$ is even. I don't know how close one can come to achieving these bounds.
Apr
3
comment Counting zero-sum free sequences of a given length in $\mathbb{Z}_n$
The link should be mathoverflow.net/questions/62764. For some reason if I put this in the text it is displayed as part of the question at this link.
Apr
3
comment Polytopes whose intersections have few vertices
@JenniferGao: no problem. It's a nice question.
Apr
3
answered Counting zero-sum free sequences of a given length in $\mathbb{Z}_n$
Apr
2
comment Polytopes whose intersections have few vertices
The unit ball is not a polytope.
Apr
2
awarded  Nice Question
Apr
1
revised Maximizing the number of semistandard Young tableaux
log(1+y-x) replaced with log(1+x-y)
Apr
1
accepted Existence of a “quasi-uniform” probablility distribution on $\mathbb{Z}$
Apr
1
asked Existence of a “quasi-uniform” probablility distribution on $\mathbb{Z}$
Mar
31
awarded  Popular Question
Mar
30
comment Identities for power series like $\sum_n z^{n^3}$
In my book Enumerative Combinatorics*, vol. 2, solution to Exercise 6.63(c), I suggest that the series $\sum_{n=0}^\infty z^{n^3}$ does not satisfy an algebraic differential equation. This would rule out a wide class of possible identities.
Mar
27
comment About structure of the set of perfect matchings of $K_{n,n}$
The matching polytope of $K_{n,n}$ leads to a "global structure" on the set of all matchings, e.g., those sets of matchings that form a face.
Mar
26
comment Positivity of Ehrhart polynomial coefficients
Another class of polytopes whose Ehrhart polynomials have nonnegative coefficients are the lattice-face polytopes of Fu Liu. See arxiv.org/abs/0810.4655. In particular, if $\mathcal{P}$ is any rational polytope, then there exists an integral polytope $\mathcal{Q}$ combinatorially equivalent to $\mathcal{P}$ such that the Ehrhart polynomial of $\mathcal{Q}$ has nonnegative coefficients.
Mar
23
comment Communal problem books
The Caltech math library had such a book. I don't know whether it still exists.