We investigate the structure of the Minkowski sum of standard simplices in R. In particular, we investigate the one-dimensional structure, the vertices, their degrees and the edges in the Minkowski sum polytope. 2000 MSC: 52B05, 52B11, 05C07.

Let A be a finite nonempty set of integers. An asymptotic estimate of several dilates sum size was obtained by Bukh. The unique known exact bound concerns the sum |A + k ·A|, where k is a prime and |A| is large. In its full generality, this bound is due to Cilleruelo, Serra and the first author. Let k be an odd prime and assume that |A| > 8kk. A corollary to our main result states that |2 · A +...

Einstein’s Equivalence Principle asserts that physical phenomena occuring in a laboratory which undergoes constant acceleration through gravity-free inertial space should be identical in all respects to that which occurs in local gravity. By incorporating special relativity theory into an extended version of the Equivalence Principle — the Special Relativistic Equivalence Principle (SREP) — pos...

Recently, Eisenbrand, Pach, Rothvoß, and Sopher studied the function M(m, n), which is the largest cardinality of a convexly independent subset of the Minkowski sum of some planar point sets P and Q with |P | = m and |Q| = n. They proved that M(m, n) = O(m2/3n2/3+m+n), and asked whether a superlinear lower bound exists for M(n, n). In this note, we show that their upper bound is the best possib...

We classify solvable Lie groups with a free nilradical admitting an Einstein left-invariant metric. Any such group is essentially determined by the nilradical of its Lie algebra, which is then called an Einstein nilradical. We show that among the free Lie algebras, there are very few Einstein nilradicals. Except for the one-step (abelian) and the two-step ones, there are only six (here f(m, p) ...

Riemannian Killing conserved currents are used to find the energy spectra of classical spinning particles moving around a spinning string in Einstein-Cartan (EC) theory of gravity. It is shown that a continuos spectrum is obtained for planar open orbits while a discrete spectrum is obtained for circular planar orbits. A spin-spin effect between the spin of the test particle and the spin of the ...

Article history: Available online 17 July 2008

The regularized four-dimensional Einstein-Gauss-Bonnet model has been recently proposed in [D. Glavan and C. Lin, Phys. Rev. Lett. \textbf{124}, 081301 (2020)] whose formulation is different of the Einstein theory, allowing us to bypass Lovelock theorem. action formulated higher dimensions ($D>4$) by adding Gauss-Bonnet correction conventional Einstein-Hilbert with a cosmological constant. spac...

We classify solvable Lie groups with free nilradical admitting an Einstein left-invariant metric. Any such group is essentially determined by the nilradical of its Lie algebra, which is then called an Einstein nilradical. We show that among the free Lie algebras, there are very few Einstein nilradicals. Except for the one-step (abelian) and the two-step ones, there are only six others: (here f(...