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4 questions
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Existence of some lattice path connecting all given lattice paths
My daily work concerns analysis on metric spaces and some time ago it turned out that the problem I am dealing with boils down to a certain combinatorial problem. I've checked a lot of examples and it ...
1
vote
1
answer
172
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Minimal volume of fundamental domains of lattices
Consider a full rank integer lattice in $\mathbb{R}^n$. Let $v_1$ be the shortest non-zero vector in the lattice, $v_2$ be the shortest one among those not parallel to $v_1$, $v_3$ be the shortest one ...
7
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2
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922
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what is the number of paths returning to 0 on the hexagonal lattice
I am looking for an estimation of the number of paths of length $n$ going from 0 to 0 on the hexagonal (or honeycomb) lattice.
I can find plenty on references on self avoiding paths, but I am looking ...
4
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2
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2k
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Can we count the number of integer lattice points in this case?
Gauss Circle problem gives the number of lattice points lie within a circle of radius $r$. This question points to a reference that estimates the number of lattice points in a $d−$dimensional ball.
$...