Following the pioneering work of Schapira, we consider topological Radon-type integral transforms on constructible Z-valued functions using the Euler characteristic as a measure. Contributions include: (1) application of the Schapira inversion formula to target localization and classification problems in sensor networks; (2) extension and application of the inversion formula to weighted Radon t...

Abstract : The main purpose of this paper is to construct the p-adic twisted (h, q)-Euler-lfunction, which interpolates generalized twisted (h, q)-Euler numbers associated with a primitive Dirichlet character χ. This is a partial answer for the open question which was remained in [13]. An application of this function leads general congruences systems for generalized twisted (h, q)Euler numbers ...

Properties of Hamiltonian symmetry flows on hyperbolic Euler-type equations are analyzed. Their Lagrangian densities are demonstrated to supply the Hamiltonian operators for subalgebras of their Noether symmetries, while substitutions between Euler-type equations define Miura transformations between the symmetry flows; some Miura maps for Liouvillean Euler-type systems are supplied by their int...

Let G be a median graph on n vertices and m edges and let k be the number of equivalence classes of the Djoković’s relation Θ defined on the edge-set of G. Then 2n − m − k ≤ 2. Moreover, 2n − m − k = 2 if and only if G is cube-free. A median graph is a connected graph such that, for every triple of vertices u, v, w, there is a unique vertex x lying on a geodesic (i.e. shortest path) between eac...

where V is the number of vertices, E is the number of edges, and F is the number of faces in the given graph, including the exterior face. This formula corresponds to the special case g = 0 (simple connectedness) of the more general Poincaré formula for genus g surfaces, in which χ ≡ χ(g) = 2− 2g. In this note we derive several analytical relations, similar to Euler’s formula, which hold for so...

Adin, Brenti, and Roichman introduced the pairs of statistics (ndes, nmaj) and (fdes, fmaj). They showed that these pairs are equidistributed over the hyperoctahedral group B n , and can be considered " Euler-Mahonian " in that they generalize the Carlitz identity. Further, they asked whether there exists a bijective proof of the equidistribution of their statistics. We give such a bijection, a...

We introduce notions of finiteness obstruction, Euler characteristic, L2-Euler characteristic, and Möbius inversion for wide classes of categories. The finiteness obstruction of a category Γ of type (FP) is a class in the projective class group K0(RΓ); the Euler characteristic and L2-Euler characteristic are respectively its RΓ-rank and L2-rank. We also extend the second author’s K-theoretic Mö...

Adin, Brenti, and Roichman introduced the pairs of statistics (ndes, nmaj) and (fdes, fmaj). They showed that these pairs are equidistributed over the hyperoctahedral group Bn, and can be considered “Euler-Mahonian” in that they generalize the Carlitz identity. Further, they asked whether there exists a bijective proof of the equidistribution of their statistics. We give such a bijection, along...

We prove that, if a geodesic metric space has Markov type 2 with constant 1, then it is an Alexandrov space of nonnegative curvature. The same technique provides a lower bound of the Markov type 2 constant of a space containing a tripod or a branching point.

Let G be an additive abelian group of finite order n and let A be a non-empty set of integers. The Davenport constant of G with weight A, DA(G), is the smallest k ∈ Z+ such that for any sequence x1, . . . , xk of elements in G, there exists a nonempty subsequence xj1 , . . . , xjr and corresponding weights a1, . . . , ar ∈ A such that �r i=1 aixji = 0. Similarly, EA(G) is the smallest positive ...