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Counting finite O-sequences of a given multiplicity.

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Τίτλος: Counting finite O-sequences of a given multiplicity.
Συγγραφείς: Cioffi, Francesca1 (AUTHOR) cioffifr@unina.it, Guida, Margherita1 (AUTHOR) maguida@unina.it
Πηγή: Applicable Algebra in Engineering, Communication & Computing. Sep2026, Vol. 37 Issue 5, p991-1002. 12p.
Θεματικοί όροι: *Multiplicity (Mathematics), *Fibonacci sequence, *Golden ratio, *Recursive sequences (Mathematics), *Combinatorics, *Mathematical sequences
Περίληψη: We study the number O d of finite O-sequences of a given multiplicity d, with particular attention to the computation of O d . We show that the sequence (O d) d is sub-Fibonacci and that, unlike the Fibonacci sequence, every term of (O d / O d - 1) d with d ≥ 6 is bounded above by the golden ratio. This analysis also produces an elementary method for computing O d . In addition, we derive an iterative formula for O d by exploiting a decomposition of lex-segment ideals introduced by S. Linusson in a previous work. [ABSTRACT FROM AUTHOR]
Βάση Δεδομένων: Academic Search Index
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  Data: Counting finite O-sequences of a given multiplicity.
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  Data: *<searchLink fieldCode="DE" term="%22Multiplicity+%28Mathematics%29%22">Multiplicity (Mathematics)</searchLink><br />*<searchLink fieldCode="DE" term="%22Fibonacci+sequence%22">Fibonacci sequence</searchLink><br />*<searchLink fieldCode="DE" term="%22Golden+ratio%22">Golden ratio</searchLink><br />*<searchLink fieldCode="DE" term="%22Recursive+sequences+%28Mathematics%29%22">Recursive sequences (Mathematics)</searchLink><br />*<searchLink fieldCode="DE" term="%22Combinatorics%22">Combinatorics</searchLink><br />*<searchLink fieldCode="DE" term="%22Mathematical+sequences%22">Mathematical sequences</searchLink>
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  Data: We study the number O d of finite O-sequences of a given multiplicity d, with particular attention to the computation of O d . We show that the sequence (O d) d is sub-Fibonacci and that, unlike the Fibonacci sequence, every term of (O d / O d - 1) d with d ≥ 6 is bounded above by the golden ratio. This analysis also produces an elementary method for computing O d . In addition, we derive an iterative formula for O d by exploiting a decomposition of lex-segment ideals introduced by S. Linusson in a previous work. [ABSTRACT FROM AUTHOR]
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      – Type: doi
        Value: 10.1007/s00200-026-00746-5
    Languages:
      – Code: eng
        Text: English
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      Pagination:
        PageCount: 12
        StartPage: 991
    Subjects:
      – SubjectFull: Multiplicity (Mathematics)
        Type: general
      – SubjectFull: Fibonacci sequence
        Type: general
      – SubjectFull: Golden ratio
        Type: general
      – SubjectFull: Recursive sequences (Mathematics)
        Type: general
      – SubjectFull: Combinatorics
        Type: general
      – SubjectFull: Mathematical sequences
        Type: general
    Titles:
      – TitleFull: Counting finite O-sequences of a given multiplicity.
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            NameFull: Cioffi, Francesca
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            NameFull: Guida, Margherita
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          Dates:
            – D: 01
              M: 09
              Text: Sep2026
              Type: published
              Y: 2026
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              Value: 37
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              Value: 5
          Titles:
            – TitleFull: Applicable Algebra in Engineering, Communication & Computing
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