Counting finite O-sequences of a given multiplicity
Abstract
We study the number Od of finite O-sequences of a given multiplicity d, with particular attention to the computation of Od. We show that the sequence (Od)d is sub-Fibonacci, and that if the sequence (Od / Od-1)d converges, its limit is bounded above by the golden ratio. This analysis also produces an elementary method for computing Od. In addition, we derive an iterative formula for Od by exploiting a decomposition of lex-segment ideals introduced by S. Linusson in a previous work.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.