NBB bases of some pattern avoiding lattices
Masaya Tomie
TL;DR
This paper determines NBB bases for certain pattern-avoiding lattices, calculates their Möbius numbers, and relates these to modified Fibonacci polynomials, advancing combinatorial understanding of these structures.
Contribution
It introduces explicit NBB bases for 123-132-213-avoiding and 321-avoiding lattices and computes their Möbius numbers, linking them to modified Fibonacci polynomials.
Findings
NBB bases are explicitly determined for the lattices.
Möbius numbers are calculated and expressed via modified Fibonacci polynomials.
Results deepen understanding of pattern-avoiding lattice structures.
Abstract
In this paper we will determine the NBB bases with respect to standard ordering of coatoms (resp.atoms) of 123-132-213-avoiding (resp.321-avoiding) lattices. Using these expression we will calculate the M\"obius numbers of 123-132-213-avoiding lattices and 321-avoiding lattices. These values become some modification of fibonacci polynomials.
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Taxonomy
TopicsAdvanced Algebra and Logic · semigroups and automata theory · Advanced Combinatorial Mathematics