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Results tagged with co.combinatorics
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user 168142
Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
10
votes
2
answers
921
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Converse to Erdős' conjecture on arithmetic progressions
I apologise in advance if this has been asked here before. I did a search and did not find anything obvious. Erdős' conjecture states that if $A\subseteq {\bf N}$ is such that $\sum_{n\in A} n^{-1}$ d …
- 807
10
votes
2
answers
378
views
Decomposing square of side length $n$ into $n$ squares in a certain "maximal" way
I was wondering if anything is known about this problem. We are given a square of side length $n$ and we wish to embed $n$ smaller (integer) squares inside it such that the sum of the side-lengths of …
- 807
2
votes
0
answers
92
views
Segre's theorem in $3$ dimensions with a "twist"
As I understand, there is a $3$-dimensional analogue of Segre's theorem stating that the maximum size of a set in ${\bf F}_q^3$ ($q$ odd) with no three points collinear is $q^2+1$. I am trying to boun …
- 807
2
votes
1
answer
110
views
Counting numerical semigroups by largest element of minimal generating set
For a given integer $n$, I am interested in the number of different numerical semigroups one can make with a generating set consisting only of integers in $[n]$.
I have done some small examples. For $ …
- 807
2
votes
1
answer
396
views
Sets with certain property concerning density of sumsets
I am working with subsets of $[n]$ of the form $(A+B)\cap A$, where $A+B$ is a sumset. Namely, I am interested if there are nonempty sets $B$ such that whenever $A$ covers a positive proportion of $[n …
- 807
1
vote
1
answer
134
views
The cap set tensor in Lovett (2019)
I hope this is appropriate for the site. I am reading the paper "The analytic rank of a tensor" [S. Lovett, Discrete Analysis (2019), #7, 10 pp.] and am a bit confused in one of the applications secti …
- 807