Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lattice simplices of maximal dimension with a given degree   It was proved by Nill that for any lattice simplex of dimension $d$ with
degree $s$ which is not a lattice pyramid, the inequality $d+1 \leq 4s-1$
holds. In this paper, we give a complete characterization of lattice simplices
satisfying the equality, i.e., the lattice simplices of dimension $(4s-2)$ with
degree $s$ which are not lattice pyramids. It turns out that such simplices
arise from binary simplex codes. As an application of this characterization, we
show that such simplices are counterexamples for the conjecture known as
"Cayley conjecture". Moreover, by modifying Nill's inequaitly slightly, we also
see the sharper bound $d+1 \leq f(2s)$, where $f(M)=\sum_{n=0}^{\lfloor \log_2
M \rfloor} \lfloor M/2^n \rfloor$ for $M \in \mathbb{Z}_{\geq 0}$. We also
observe that any lattice simplex attaining this sharper bound always comes from
a binary code.

26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: eess
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
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The categories of this paper are: comp-gas