Ahmed, C., Martin, P. orcid.org/0000-0002-8141-9465 and Mazorchuk, V. (2021) On the number of principal ideals in d-tonal partition monoids. Annals of Combinatorics, 25 (1). pp. 79-113. ISSN 0218-0006
Abstract
For a positive integer d, a non-negative integer n and a non-negative integer h≤ n, we study the number Cn(d) of principal ideals; and the number Cn,h(d) of principal ideals generated by an element of rank h, in the d-tonal partition monoid on n elements. We compute closed forms for the first family, as partial cumulative sums of known sequences. The second gives an infinite family of new integral sequences. We discuss their connections to certain integral lattices as well as to combinatorics of partitions.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2021 The Author(s). This is an open access article under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits unrestricted use, distribution and reproduction in any medium, provided the original work is properly cited. |
Keywords: | Partition monoid, Principal ideal, Rank, Integer sequence, Hollow hexagon, Tiling |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Funding Information: | Funder Grant number EPSRC (Engineering and Physical Sciences Research Council) EP/L001152/1 EPSRC (Engineering and Physical Sciences Research Council) EP/I038683/1 |
Depositing User: | Symplectic Publications |
Date Deposited: | 07 Jan 2025 10:36 |
Last Modified: | 07 Jan 2025 10:36 |
Status: | Published |
Publisher: | Springer |
Identification Number: | 10.1007/s00026-020-00518-z |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:221425 |