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On the number of pr...
On the number of principal ideals in d-tonal partition monoids
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- Ahmed, Chwas (author)
- Univ Leeds, Dept Pure Math, Leeds LS2 9JT, England.;Univ Sulaimani, Coll Sci, Dept Math, Sulaimani, Iraq.
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- Martin, Paul (author)
- Univ Leeds, Dept Pure Math, Leeds LS2 9JT, England.
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- Mazorchuk, Volodymyr (author)
- Uppsala universitet,Algebra och geometri
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Univ Leeds, Dept Pure Math, Leeds LS2 9JT, England;Univ Sulaimani, Coll Sci, Dept Math, Sulaimani, Iraq. Univ Leeds, Dept Pure Math, Leeds LS2 9JT, England. (creator_code:org_t)
- 2021-01-08
- 2021
- English.
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In: Annals of Combinatorics. - : Springer. - 0218-0006 .- 0219-3094. ; 25:1, s. 79-113
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Abstract
Subject headings
Close
- For a positive integer d, a non-negative integer n and a non-negative integer h <= n, we study the number C-n((d)) of principal ideals; and the number C-n,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.
Subject headings
- TEKNIK OCH TEKNOLOGIER -- Elektroteknik och elektronik -- Kommunikationssystem (hsv//swe)
- ENGINEERING AND TECHNOLOGY -- Electrical Engineering, Electronic Engineering, Information Engineering -- Communication Systems (hsv//eng)
Keyword
- Partition monoid
- Principal ideal
- Rank
- Integer sequence
- Hollow hexagon
- Tiling
Publication and Content Type
- ref (subject category)
- art (subject category)
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