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1 Journal of Mathematics and Applications

1 2023

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Bayer Noise symmetric functions and some combinatorial algebraic structures

Abdulwahid Adnan Hashim, Elamami Elgaddafi

Journal of Mathematics and Applications

2023

Vol. 46

115--148

Symmetric functions play a crucial role in classifying representations of symmetric groups, and they are largely involved with combinatorial algebras and graph theory. Bayer filter technique is largely applied in most of the professional digital cameras due to the fact that it is a low-cost, and it allows photosensors not only to capture the intensity of light, but also to record the wavelength of light as well. Using Bayer Pattern, we introduce the Bayer Noise symmetric functions and the Bayer Noise Schur functions, and we study some combinatorial structures on the Bayer Noise modules. We study the connection between Bayer Noise symmetric functions and other bases for the algebra of symmetric functions, and we explicitly calculate special cases over a fixed commutative ring k. We also study the compatibility of such algebraic and coalgebraic structures.