ﻻ يوجد ملخص باللغة العربية
A clean lattice triangle in ${mathbb R}^2$ is a triangle that does not contain any lattice points on its sides other than its vertices. The central goal of this paper is to count the number of clean triangles of a given area up to unimodular equivalence. In doing so we use a variant of the Euler phi function which we call $imph(n)$ (imitation phi).
We illustrate the application of the matrix-transfer method for a number of enumeration problems concerning the party game Silent Circles, Hamiltonian cycles in the antiprism graphs, and simple paths and cycles of a fixed length in arbitrary graphs.
We use a sign-reversing involution to show that trees on the vertex set [n], considered to be rooted at 1, in which no vertex has exactly one child are counted by 1/n sum_{k=1}^{n} (-1)^(n-k) {n}-choose-{k} (n-1)!/(k-1)! k^(k-1). This result corrects
Regular tree grammars and regular path expressions constitute core constructs widely used in programming languages and type systems. Nevertheless, there has been little research so far on frameworks for reasoning about path expressions where node car
The counting of pairs of galaxies or stars according to their distance is at the core of all real-space correlation analyzes performed in astrophysics and cosmology. The next stage upcoming ground (LSST) and space (Euclid) surveys will measure proper
The Exact Satisfiability problem, XSAT, is defined as the problem of finding a satisfying assignment to a formula in CNF such that there is exactly one literal in each clause assigned to be 1 and the other literals in the same clause are set to 0. If