Lattice paths , re ections , & dimension - changing bijectionsRichard
نویسندگان
چکیده
We enumerate various families of planar lattice paths consisting of unit steps in directions N, S, E, or W, which do not cross the x-axis or both x-and y-axes. The proofs are purely combinatorial throughout, using either reeections or bijections between these NSEW-paths and linear NS-paths. We also consider other dimension-changing bijections.
منابع مشابه
The Leech Lattice and Complex Hyperbolic Re ections
We construct a natural sequence of nite-covolume reeection groups acting on the complex hy-perbolic spaces C H 13 , C H 9 and C H 5 , and show that the 9-dimensional example coincides with the largest of the groups of Mostow 10]. These reeection groups arise as automorphism groups of certain Lorentzian lattices over the Eisenstein integers, and we obtain our largest example by using the complex...
متن کاملModeling re ections with an elastic screen method
This paper gives two versions of elastic screen method The wide angle version has a better accuracy while the small angle approximation is more e cient The accu racy of the re ectivity is discussed by comparing the analytical results from the screen method and those directly from plane wave re ections The accuracy of waveform is checked by comparing synthetic seis mograms from both screen metho...
متن کاملNonre ecting Boundary Conditions for Linear Hyperbolic Systems 1
Many compressible ow and aeroacoustic computations rely on accurate nonre ecting or radiation boundary conditions. When the equations and boundary conditions are discretized using a nite-di erence scheme, the dispersive nature of the discretized equations can lead to spurious numerical re ections not seen in the continuous boundary value problem. Here we construct discretely nonre ecting bounda...
متن کاملPhase transition of KDP observed by Resonant X-ray Diffraction at forbidden reflections
We report observations of space-group-forbidden Bragg re ections in Potassium Dihydrogen Phosphate (KH2PO4), also known as KDP, measured by resonant x-ray di raction at the potassium K edge. We nd clear evidence for a transition from one class of space-groupforbidden re ections, where scattering is ruled out by the electric dipole approximation, to a second class, in the ferroelectric phase, wh...
متن کامل3D Reconstruction of Skin Surface from Image Sequence
This paper proposes a new method for reconstruction a shape of skin surface replica from shading image sequence taken with di erent light source directions. Since the shading images include shadows caused by surface height uctuation, and specular and inter re ections, the conventional photometric stereo method is not suitable for reconstructing its surface accurately. In the proposed method, we...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1992