Generating tree method and applications to pattern-avoiding inversion sequences
| buir.advisor | Yıldırım, Gökhan | |
| dc.contributor.author | Gezer, Melis | |
| dc.date.accessioned | 2024-06-13T10:38:48Z | |
| dc.date.available | 2024-06-13T10:38:48Z | |
| dc.date.copyright | 2024-05 | |
| dc.date.issued | 2024-05 | |
| dc.date.submitted | 2024-06-12 | |
| dc.department | Department of Mathematics | |
| dc.description | Cataloged from PDF version of article. | |
| dc.description | Thesis (Master's): Bilkent University, Department of Mathematics, İhsan Doğramacı Bilkent University, 2024. | |
| dc.description | Includes bibliographical references (leave 97-99). | |
| dc.description.abstract | An inversion sequence of length n is an integer sequence e = e1 · · · en such that 0 ≤ ei < i for each 0 ≤ i ≤ n. We use In to denote the set of inversion sequences of length n. Let [k] := {0, 1, · · · , k − 1} denote the alphabet and τ be a word of length k over this alphabet. A pattern of length k is simply a word over the alphabet [k]. We say an inversion sequence e ∈ In contains the pattern τ of length k if it contains a sub-sequence of length k that is order isomorphic to τ; otherwise, e avoids the pattern τ . For a given pattern τ , we use In(τ ) to denote the set of all τ -avoiding inversion sequences of length n. Firstly, we review the enumeration of inversion sequences that avoid patterns of length three. We then study an enumeration method based on generating trees and the kernel method to enumerate pattern-avoiding inversion sequences for general patterns. Then, we provide sampling algorithms for pattern-avoiding inversion sequences and apply them to some specific patterns. Based on extensive simulations, we study some statistics such as the number of zeros, the number of distinct elements, the number of repeated elements, and the maximum elements. Finally, we present a bijection between In(0312) and In(0321) that preserves these statistics. | |
| dc.description.degree | M.S. | |
| dc.description.statementofresponsibility | by Melis Gezer | |
| dc.format.extent | x, 99 leaves : charts ; 30 cm. | |
| dc.identifier.itemid | B124742 | |
| dc.identifier.uri | https://hdl.handle.net/11693/115199 | |
| dc.language.iso | English | |
| dc.publisher | Bilkent University | |
| dc.rights | info:eu-repo/semantics/openAccess | |
| dc.subject | Inversion sequences | |
| dc.subject | Pattern avoidance | |
| dc.subject | Generating functions | |
| dc.subject | Generating trees | |
| dc.subject | Kernel method | |
| dc.subject | Random sampling | |
| dc.title | Generating tree method and applications to pattern-avoiding inversion sequences | |
| dc.title.alternative | Üreteç ağaçlar yöntemi ve motif içermeyen ters-çevrim dizilerine uygulamaları | |
| dc.type | Thesis |