We fix n and say a square in the two-dimensional grid indexed by (x, y) has color c if x+ y ≡ c (mod n). A ribbon tile of order-n is a connected polyomino containing exactly one square of each color. We show that the set of order-n ribbon tilings of a simply connected region R is in one-to-one correspondence with a set of height functions from the vertices of R to Zn satisfying certain differen...

A motivic height zeta function associated to a family of varieties parametrised by curve is the generating series classes, in Grothendieck ring varieties, moduli spaces sections this with varying degrees. This text devoted study generic fiber having structure an equivariant compactification vector group. Our main theorem describes convergence respect topology on coming from theory weights cohom...

one of the most important problems in geodesy is the unification of height datum. generally in geodesy; there are two types of height systems, the geometrical height based on ellipsoid and the physical height based on gravity-defined surface (zhang et al, 2009).local height datum is determined according to mean sea level (msl). in regarding to mismatch of mean sea level and geoid, on the one ha...