Bayer Noise symmetric functions and some combinatorial algebraic structures

• Autorzy: Abdulwahid Adnan Hashim , Elamami Elgaddafi

Identyfikatory

DOI

10.7862/rf.2023.5

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

symmetric functions; Schur functions; algebra; coalgebra; noise

PL

funkcje symetryczne; funkcje Schura; algebra; hałas

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Journal of Mathematics and Applications
• Rocznik: 2023
• Tom: Vol. 46
• Strony: 115--148
• Opis fizyczny: Bibliogr. 11 poz., rys., tab.

Twórcy

autor

Abdulwahid Adnan Hashim

• College of Business, Engineering, and Technology, Texas A & M University-Texarkana, 7101 University Ave, Texarkana, TX, 75503, USA

• https://orcid.org/0000-0002-4885-7770

autor

Elamami Elgaddafi

• University of St. Thomas, 3800 Montrose Blvd, Houston, TX 77006, USA

• https://orcid.org/0009-0002-3250-3481

Bibliografia

• [1] D. R. Bull, Communicating pictures. A Course in Image and Video Coding, New York, NY, USA, Academic Press, 2014.
• [2] D. Grinberg. V. Reiner. Hopf Algebras in Combinatorics, Lecture notes, Vrije Universiteit Brussel, 2020. https://www.cip.ifi.lmu.de/~grinberg/algebra/HopfComb.pdf
• [3] I. G. Macdonald, Symmetric Functions and Hall Polynomials, 2nd edition, Oxford University Press, Oxford-New York, 1995.
• [4] P. L. Méliot, Representation Theory of Symmetric Groups, Discrete Mathematics and its Applications, CRC Press, 2017.
• [5] A. Mendes, J. Remmel, Counting with Symmetric Functions, Developments in Mathematics 43, Springer, 2015.
• [6] D. Paliya, A. Foia, R. Bilcub, V. Katkovnika, Denoising and interpolation of noisy bayer data with adaptive cross-color filters, In: Proc. of SPIE VCIP (2008).
• [7] J. F. Peters, Topology of Digital Images, Visual Pattern Discovery in Proximity Spaces, Intelligent Systems Reference Library, 63, Springer, Berlin, 2014.
• [8] B. E. Sagan, Combinatorics: The Art of Counting, Draft of a textbook, 2020. https://users.math.msu.edu/users/bsagan/Books/Aoc/aoc.pdf.
• [9] S. V. Sam, Notes for Math 740 (Symmetric Functions), 27 April 2017. https://www.math.wisc.edu/~svs/740/notes.pdf
• [10] R. P. Stanley, Enumerative Combinatorics, Volumes 1 and 2, Cambridge Studies in Advanced Mathematics 49 and 62, Cambridge University Press, Cambridge, 2nd edition 2011 (volume 1) and 1st edition 1999 (volume 2).
• [11] M. Wildon, An Involutive Introduction to Symmetric Functions, 1 July 2017. http://www.ma.rhul.ac.uk/~uvah099/teaching.html

Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).