WATER CELLS IN COMPOSITIONS OF 1S AND 2S
Issued Date
2025-05-01
Resource Type
ISSN
00150517
Scopus ID
2-s2.0-105016116705
Journal Title
Fibonacci Quarterly
Volume
63
Issue
2
Start Page
400
End Page
411
Rights Holder(s)
SCOPUS
Bibliographic Citation
Fibonacci Quarterly Vol.63 No.2 (2025) , 400-411
Suggested Citation
Hopkins B., Tangboonduangjit A. WATER CELLS IN COMPOSITIONS OF 1S AND 2S. Fibonacci Quarterly Vol.63 No.2 (2025) , 400-411. 411. doi:10.1080/00150517.2025.2513335 Retrieved from: https://repository.li.mahidol.ac.th/handle/123456789/112228
Title
WATER CELLS IN COMPOSITIONS OF 1S AND 2S
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Author's Affiliation
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Abstract
Mansour and Shattuck introduced the notion of water cells for integer compositions in 2018. We focus on compositions with parts restricted to 1 and 2 and consider the array of counts for such compositions of n with k water cells, establishing generating functions for the columns and diagonal sums, recurrences within the array in the spirit of Pascal’s lemma, and connections to other restricted compositions. Most of our proofs are combinatorial, but we also make use of Riordan arrays.