Gram matrices and Stirling numbers of a class of diagram algebras, I

In this paper, we introduce Gram matrices for the signed partition algebras, the algebra of \(\mathbb{Z}_2\)-relations and the partition algebras. The nondegeneracy and symmetic nature of these Gram matrices are establised. Also, \((s_1, s_2, r_1, r_2, p_1, p_2)\)-Stirling numbers of the second kind...

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Date:	2018
Main Authors:	Karimilla Bi, N., Parvathi, M.
Format:	Article
Language:	English
Published:	Lugansk National Taras Shevchenko University 2018
Subjects:	Gram matrices partition algebras signed partition algebras and the algebra of \(\mathbb{Z}_2\)-relations 16Z05
Online Access:	https://admjournal.luguniv.edu.ua/index.php/adm/article/view/36
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Journal Title:	Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics

id	oai:ojs.admjournal.luguniv.edu.ua:article-36
record_format	ojs
spelling	oai:ojs.admjournal.luguniv.edu.ua:article-362018-05-17T07:54:05Z Gram matrices and Stirling numbers of a class of diagram algebras, I Karimilla Bi, N. Parvathi, M. Gram matrices, partition algebras, signed partition algebras and the algebra of \(\mathbb{Z}_2\)-relations 16Z05 In this paper, we introduce Gram matrices for the signed partition algebras, the algebra of \(\mathbb{Z}_2\)-relations and the partition algebras. The nondegeneracy and symmetic nature of these Gram matrices are establised. Also, \((s_1, s_2, r_1, r_2, p_1, p_2)\)-Stirling numbers of the second kind for the signed partition algebras, the algebra of \(\mathbb{Z}_2\)-relations are introduced and their identities are established. Stirling numbers of the second kind for the partition algebras are introduced and their identities are established. Lugansk National Taras Shevchenko University 2018-04-27 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/36 Algebra and Discrete Mathematics; Vol 25, No 1 (2018) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/36/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/36/331 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/36/332 Copyright (c) 2018 Algebra and Discrete Mathematics
institution	Algebra and Discrete Mathematics
baseUrl_str
datestamp_date	2018-05-17T07:54:05Z
collection	OJS
language	English
topic	Gram matrices partition algebras signed partition algebras and the algebra of \(\mathbb{Z}_2\)-relations 16Z05
spellingShingle	Gram matrices partition algebras signed partition algebras and the algebra of \(\mathbb{Z}_2\)-relations 16Z05 Karimilla Bi, N. Parvathi, M. Gram matrices and Stirling numbers of a class of diagram algebras, I
topic_facet	Gram matrices partition algebras signed partition algebras and the algebra of \(\mathbb{Z}_2\)-relations 16Z05
format	Article
author	Karimilla Bi, N. Parvathi, M.
author_facet	Karimilla Bi, N. Parvathi, M.
author_sort	Karimilla Bi, N.
title	Gram matrices and Stirling numbers of a class of diagram algebras, I
title_short	Gram matrices and Stirling numbers of a class of diagram algebras, I
title_full	Gram matrices and Stirling numbers of a class of diagram algebras, I
title_fullStr	Gram matrices and Stirling numbers of a class of diagram algebras, I
title_full_unstemmed	Gram matrices and Stirling numbers of a class of diagram algebras, I
title_sort	gram matrices and stirling numbers of a class of diagram algebras, i
description	In this paper, we introduce Gram matrices for the signed partition algebras, the algebra of \(\mathbb{Z}_2\)-relations and the partition algebras. The nondegeneracy and symmetic nature of these Gram matrices are establised. Also, \((s_1, s_2, r_1, r_2, p_1, p_2)\)-Stirling numbers of the second kind for the signed partition algebras, the algebra of \(\mathbb{Z}_2\)-relations are introduced and their identities are established. Stirling numbers of the second kind for the partition algebras are introduced and their identities are established.
publisher	Lugansk National Taras Shevchenko University
publishDate	2018
url	https://admjournal.luguniv.edu.ua/index.php/adm/article/view/36
work_keys_str_mv	AT karimillabin grammatricesandstirlingnumbersofaclassofdiagramalgebrasi AT parvathim grammatricesandstirlingnumbersofaclassofdiagramalgebrasi
first_indexed	2025-07-17T10:31:14Z
last_indexed	2025-07-17T10:31:14Z
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Gram matrices and Stirling numbers of a class of diagram algebras, I

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