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### the maximal length of a special dicksonian sequence

First, we define a sequence $t_{1},t_{2},\cdots,t_{k}$ of n-tuples dicksonian, if $\forall 1\leq i < j\leq k,$ there does not exist a non-negative n-tuple t such that
$t_{i}+t=t_{j}.$ For example, ...

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### A non-associative three-valued logic

There are three elements: x, y, z and a relation C:
x C y, y C z, z C x, x C x, y C y, z C z.
Let us introduce two binary operations with respect to the C: "the leftmost" (L) and "the rightmost" ...

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### recursion formula for odd holonomic function

suppose we have a map
$f:\mathbb{Z}\longrightarrow\mathbb{C}[t^{\pm}]$
with property that $f(i)=-f(-i)$.
The algebra
$\mathcal{T}=\mathbb{C}[t^{\pm}][L^{\pm},M^{\pm}]/[LM=tML]$ acts on $f$ by
...

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### Is there a discrete Cerf theory?

Towards the end of the 1990's, Robin Forman developed a discrete version of Morse theory, which concerns maps from a simplicial complex to $\mathbb{R}$ satisfying a combinatorial analogue to the ...

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### Domination in Nice Lattices

Let an integer vector be nice when it has only two nonzero components, which sum to zero. So (0, 0, 3, 0, -3) and (-1, 0, 1, 0, 0) are examples of nice vectors in $n=5$ dimensions.
Call a lattice ...

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### 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 ...

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### 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 ...

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### 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 ...

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### 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)]} ...

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### 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 ...