Bayer noise quasisymmetric functions andsome combinatorial algebraic structures

Recently, quasisymmetric functions have been widely studieddue to their big connection to enumerative combinatorics, combinatorial Hopfalgebra and number theory. The Bayer filter mosaic, named due to BryceBayer (1929-2012), is a color filter array used to arrange RGB color filterson a square grid of photosensors. It is the most common pattern of filters,and almost all professional digital cameras are applications of this filter. Weuse this filter to introduce the Bayer Noise quasisymmetric functions, andwe study some combinatorial algebraic and coalgebraic structures on Quasi-Bayer Noise modules and on Quasi-Bayer GB-Noise modules. We explicitlydescribe the primitive basis elements for each comultiplication defined onQuasi-Bayer Noise modules, and we calculate different kinds of comultiplica-tions defined on Quasi-Bayer Noises module over a fixed commutative ringk.