|
|||||
 |
|
|
|
|
|
|
|
Catalan
recursion on externally ordered bases of unit interval
positroids
Jan Tracy Camacho and Anastasia Chavez
Vol. 14 (2021), No. 5, 893–905
|
Abstract |
|
The Catalan numbers form a sequence that counts over 200 combinatorial objects. A remarkable property of the Catalan numbers, which extends to these objects, is its recursive definition; that is, we can determine the -th object from previous ones. A matroid is a combinatorial object that generalizes the notion of linear independence with connections to many fields of mathematics. A family of matroids, called unit interval positroids (UIP), are Catalan objects induced by the antiadjacency matrices of unit interval orders. Associated to each UIP is the set of externally ordered bases, which due to Las Vergnas, produces a lattice after adjoining a bottom element. We study the poset of externally ordered UIP bases and the implied Catalan-induced recursion. Explicitly, we describe an algorithm for constructing the lattice of a rank- UIP from the lattice of lower ranks. Using their inherent combinatorial structure, we define a simple formula to enumerate the bases for a given UIP. |
PDF Access Denied
We have not been able to recognize your IP address
18.222.67.251
as that of a subscriber to this journal.
Online access to the content of recent issues is by
subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form. Or, visit our subscription page for instructions on purchasing a subscription.
You may also contact us at
contact@msp.org
or by using our
contact form.
Or, you may purchase this single article for USD 30.00:
Keywords
matroid, positroid, Catalan number, Catalan recursion,
poset
|
Mathematical Subject Classification
Primary: 05B35
|
Supplementary material |
Milestones
Received: 29 April 2021
Revised: 1 June 2021
Accepted: 2 June 2021
Published: 9 February 2022
Communicated by Stephan Garcia
|
Authors |
| Jan Tracy Camacho | |
| Department of Mathematics San Francisco State University San Francisco, CA United States |
|
| Anastasia Chavez | |
| Department of Mathematics and
Computer Science Saint Mary’s College of California Moraga, CA United States |
|
