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14
votes
3answers
791 views

Partitioning the integers $1$ through $n$ so that the product of the elements in one set is equal to the sum of the elements in the other

I asked this question at math.SE a couple of months ago and only got a partial answer, so I thought I would try here. It is known that, for $n \geq 5$, it is possible to partition the integers ...
8
votes
2answers
1k views

palindromic subsequences

I'd like any insight or references to the following two conjectures (see the glossary below for definitions): Conjecture 1: For any string $x$, there exists a longest common subsequence of $x$ and ...
7
votes
9answers
441 views

What are some early examples of creation of lists / catalogues of (particularly) combinatorial objects?

A lot of effort in discrete maths / combinatorics is expended in the construction of lists, catalogues or census [sic] of combinatorial objects such as groups, graphs, designs etc. These catalogues ...
1
vote
0answers
426 views

Zeroes of a tricky function.

I am attempting to show that there does not exist an N past which every open unit interval (k, k+1) -where k is an integer- contains a zero of the following function: $h(x)=\sum_{n=2}^{[\sqrt(x)]} ...
7
votes
3answers
983 views

How to characterize a Self-avoiding path.

I cannot find any answer to that apparently simple problem : On a square lattice, a path is given by a sequence of relative moves in {"move forward", "turn right" and "turn left"}. Is there a rule ...