Arrangement Of Letters In Words Using Parikh Matrices

The Parikh matrix mapping is an ingenious generalization of the classical Parikh mapping in the aim to arithmetize words by numbers. Two words are M-equivalent if and only if they share the same Parikh matrix. The characterization of M-equivalent words remains open even for the case of the ternary...

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Main Author:	Poovanandran, Ghajendran
Format:	Thesis
Language:	English
Published:	2019
Subjects:	QA184-205 Linear and Multilinear Algebra Matrices
Online Access:	http://eprints.usm.my/61141/1/Arrangement%20of%20letters%20in%20words%20cut.pdf
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id	my-usm-ep.61141
record_format	uketd_dc
spelling	my-usm-ep.611412024-09-18T02:39:37Z Arrangement Of Letters In Words Using Parikh Matrices 2019-04 Poovanandran, Ghajendran QA184-205 Linear and Multilinear Algebra, Matrices The Parikh matrix mapping is an ingenious generalization of the classical Parikh mapping in the aim to arithmetize words by numbers. Two words are M-equivalent if and only if they share the same Parikh matrix. The characterization of M-equivalent words remains open even for the case of the ternary alphabet. Due to the dependency of Parikh matrices on the ordering of the alphabet, the notion of strong M-equivalence was proposed as an order-independent alternative to M-equivalence. In this work, we introduce a new symmetric transformation that justifies strong M-equivalence for the ternary alphabet. We then extend certain work of §erbanuja to the context of strong equivalence and show that the number of strongly M-unambiguous prints for any alphabet is always finite. 2019-04 Thesis http://eprints.usm.my/61141/ http://eprints.usm.my/61141/1/Arrangement%20of%20letters%20in%20words%20cut.pdf application/pdf en public phd doctoral Universiti Sains Malaysia Pusat Pengajian Sains Matematik
institution	Universiti Sains Malaysia
collection	USM Institutional Repository
language	English
topic	QA184-205 Linear and Multilinear Algebra Matrices
spellingShingle	QA184-205 Linear and Multilinear Algebra Matrices Poovanandran, Ghajendran Arrangement Of Letters In Words Using Parikh Matrices
description	The Parikh matrix mapping is an ingenious generalization of the classical Parikh mapping in the aim to arithmetize words by numbers. Two words are M-equivalent if and only if they share the same Parikh matrix. The characterization of M-equivalent words remains open even for the case of the ternary alphabet. Due to the dependency of Parikh matrices on the ordering of the alphabet, the notion of strong M-equivalence was proposed as an order-independent alternative to M-equivalence. In this work, we introduce a new symmetric transformation that justifies strong M-equivalence for the ternary alphabet. We then extend certain work of §erbanuja to the context of strong equivalence and show that the number of strongly M-unambiguous prints for any alphabet is always finite.
format	Thesis
qualification_name	Doctor of Philosophy (PhD.)
qualification_level	Doctorate
author	Poovanandran, Ghajendran
author_facet	Poovanandran, Ghajendran
author_sort	Poovanandran, Ghajendran
title	Arrangement Of Letters In Words Using Parikh Matrices
title_short	Arrangement Of Letters In Words Using Parikh Matrices
title_full	Arrangement Of Letters In Words Using Parikh Matrices
title_fullStr	Arrangement Of Letters In Words Using Parikh Matrices
title_full_unstemmed	Arrangement Of Letters In Words Using Parikh Matrices
title_sort	arrangement of letters in words using parikh matrices
granting_institution	Universiti Sains Malaysia
granting_department	Pusat Pengajian Sains Matematik
publishDate	2019
url	http://eprints.usm.my/61141/1/Arrangement%20of%20letters%20in%20words%20cut.pdf
_version_	1811772885022277632

Arrangement Of Letters In Words Using Parikh Matrices

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