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Title: Combinatorial Results on Barcode Lattices
Abstract A barcode is a finite multiset of intervals on the real line. Jaramillo-Rodriguez (2023) previously defined a map from the space of barcodes with a fixed number of bars to a set of multipermutations, which presented new combinatorial invariants on the space of barcodes. A partial order can be defined on these multipermutations, resulting in a class of posets known as combinatorial barcode lattices. In this paper, we provide a number of equivalent definitions for the combinatorial barcode lattice, show that its Möbius function is a restriction of the Möbius function of the symmetric group under the weak Bruhat order, and show its ground set is the Jordan-Hölder set of a labeled poset. Furthermore, we obtain formulas for the number of join-irreducible elements, the rank-generating function, and the number of maximal chains of combinatorial barcode lattices. Lastly, we make connections between intervals in the combinatorial barcode lattice and certain classes of matchings.  more » « less
Award ID(s):
1928930 2102921
PAR ID:
10528405
Author(s) / Creator(s):
;
Publisher / Repository:
Springer Science + Business Media
Date Published:
Journal Name:
Order
Volume:
42
Issue:
1
ISSN:
0167-8094
Format(s):
Medium: X Size: p. 193-209
Size(s):
p. 193-209
Sponsoring Org:
National Science Foundation
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