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On the Frobenius norms of circulant matrices with Ducci sequences and Narayana and Gaussian Narayana numbers.

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Bibliographic Details
Title:	On the Frobenius norms of circulant matrices with Ducci sequences and Narayana and Gaussian Narayana numbers.
Authors:	BALA, Roji, MISHRA, Vinod
Source:	Communications Series A1 Mathematics & Statistics; 2025, Vol. 74 Issue 3, p460-477, 18p
Subject Terms:	CIRCULANT matrices, MATRIX norms, MATRICES (Mathematics), COMBINATORICS, DECODING algorithms
Abstract:	In the present paper, we obtain identities for Narayana numbers, like the sum of terms with even and odd subscripts, the sum of products of consecutive terms and the sum of squares of terms. Then, we find images DN and D²N of n-tuple N = (N1, N2, N3, ..., Nn) of Narayana numbers under a map D: C → C defined as D(z1, z2, ..., zn) = (\|z2 - z1\|, \|z3 - z2\|, ..., \|zn - zn-1\|, \|zn - z1\|). We are then determined the circulant, skew-circulant, and semi-circulant matrices of these images. We have been discovered Frobenius norms of these circulant matrices and relations among these norms. In addition, we find DG and D²G by taking the n-tuple G = (GN1, GN2, ..., GNn) of Gaussian Narayana numbers. After that, we create circulant, semi-circulant, and skew-circulant matrices of G, DG, D²G, determine their Frobenius norms, and derive relationships between them. Then, we obtain relations between norms of matrices of Narayana numbers and Gaussian Narayana numbers. Finally, coding and decoding methods with the use of circulant matrices of Narayana numbers and Gaussian Narayana numbers have been introduced. [ABSTRACT FROM AUTHOR]
	Copyright of Communications Series A1 Mathematics & Statistics is the property of Ankara University and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database:	Complementary Index

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