A closer look at some new identities by Geoffrey B. Campbell

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Visible point vector summations from hypercube and hyperpyramid lattices by Geoffrey B. Campbell

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A new class of infinite products, and Euler's totient by Geoffrey B. Campbell

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Positive Solutions of a General Discrete Dirichlet Boundary Value Problem by Xinfu Li, Guang Zhang

“…All obtained results are new and valid on any n-dimension finite lattice point domain. To the best of our knowledge, they are better than the results of the corresponding partial differential equations. …”
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Pick’s Theorem in Two-Dimensional Subspace of R3 by Lin Si

“…For any two-dimensional simple lattice polygon P, we establish the following analogy version of Pick’s Theorem, kIP+1/2BP-1, where BP is the number of lattice points on the boundary of P in Z3, IP is the number of lattice points in the interior of P in Z3, and k is a constant only related to the two-dimensional subspace including P.…”
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Empty simplices of large width by Joseph Doolittle, Lukas Katthän, Benjamin Nill, Francisco Santos

“…An empty simplex is a lattice simplex in which vertices are the only lattice points. We show two constructions leading to the first known empty simplices of width larger than their dimension: ◦ We introduce cyclotomic simplices and exhaustively compute all the cyclotomic simplices of dimension $10$ and volume up to $2^{31}$ . …”
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