# 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.

1,579 questions
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### Does anyone know of this manifestation of the Littlewood-Richardson coefficients for the complete flag variety?

This is the culmination of about 11 years of research but after I discovered it I found a proof that was extremely trivial, so I'm wondering if it's already known. Let $(a,b)$ with $a < b$ ...
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### Counting symmetric subgroups of symmetric groups

This question is related to, but much more specific than, this one. For $k \leq n$, let $a(k,n)$ denote the number of conjugacy classes of subgroups of the symmetric group $S_n$ which are isomorphic ...
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### Nonzero subdeterminants conjecture: has anybody seen this anywhere?

I already posted this question on Mathematics StackExchange. A user there suggested that I rather post it on mathoverflow, since it is a research question. So here it is. Let $m\geq2$, $n\geq1$ be ...
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### Is recognizing if a Latin square is isotopic to its transpose more efficient than computing its symmetry group?

Ihrig and Ihrig (2007) described a mathematical method for determining if a Latin square is isotopic to its transpose (where isotopic Latin squares vary by permuting the rows, columns and symbols). ...
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### A strong sum-product “for translates” in finite fields

In the course of some recent research, I've sketched out a proof of the following result. My basis question is: is the result interesting? Proposition There exists an absolute constant $c$ such ...
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### Erdös-Fuchs Theorem for multivariate linear forms

Let $A$ be an infinite set of positive integers, and denote by $r(n)$ the number of solutions to the equation $a+a'=n$, with $a,\, a' \in A$. It is not very difficult to show that if $r(n) > 0$ ...
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### A Product Related to Partitions with Largest Part n

This is a finite version of a problem of mine entitled "A product related to unrestricted partitions." It has the advantage that, at least for small values of n, it is easily solved. Begin with the ...
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### Generalised Polya's urn with i.i.d. replacement

Let $\mu$ be a fixed measure (possibly with moment conditions) on $\mathbb N$ and $X_1,X_2,\dots$ be i.i.d. samples from $\mu$. Start with one white and one black ball in the urn. At the $n$-th step, ...
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### Generalized flag complex?

Assume we glue an $n$-dimensional simplicial complex $K$ from copies of an $n$-simplex $\Delta$ with fixed spherical metric. We may think that $\Delta$ has colored vertices and we glue so that the ...
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### What are the known algorithms for computing the inverse of a group automorphism?

Given a finitely presented group $<x_1,x_2,...,x_n|R_1,R_2,...,R_n>$, one specifies an automorphism $\phi$ by its action on the generators, i.e. $\phi(x_i)=w_i$ for some (reduced) words $w_i$ in ...
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### det(A)det(B) = det(AB+correction), Capelli identities, “factorized” representation of $\mathfrak {gl}_n$

Context: Some probably know that there are Capelli identities which state $$det(A)det(B) = det(AB+correction)$$ for some matrices with non-commuting elements, they go back to the 19-th century, but ...
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### Motivation behind Panyushev's “constant-averages-along-orbits” conjecture

In his article "On orbits of antichains of positive roots" (European Journal of Combinatorics 30 (2009) 586–594; sorry, it's an Elsevier journal, so there's no freely available online version for me ...
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### Can one give a “nice” expression for this determinant?

I am asking this question on behalf of a senior faculty member who is sometimes intimidated by computers. It is motivated by a problem in invariant theory. Unfortunately the question is a bit vague. ...