Labeled Chip-Firing on Binary Trees with 2 n- 1 Chips

Gregg Musiker; Son Nguyen

doi:10.1007/s00026-023-00680-0

Labeled Chip-Firing on Binary Trees with 2 ⁿ- 1 Chips

Gregg Musiker, Son Nguyen

School of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We study labeled chip-firing on binary trees starting with 2ⁿ-1 chips initially placed at the root. We prove a sorting property of terminal configurations of the process. We also analyze the end game moves poset and prove that this poset is a modular lattice.

Original language	English (US)
Pages (from-to)	1167-1197
Number of pages	31
Journal	Annals of Combinatorics
Volume	28
Issue number	4
DOIs	https://doi.org/10.1007/s00026-023-00680-0
State	Published - Dec 2024

Bibliographical note

Publisher Copyright:
© The Author(s), under exclusive licence to Springer Nature Switzerland AG 2023.

Keywords

Binary tree
Confluence
Labeled chip-firing
Lattice poset

Publisher link

10.1007/s00026-023-00680-0

Find It

Find It at U of M Libraries

Cite this

@article{daf28a4f578548028f9253b4c1ba6451,

title = "Labeled Chip-Firing on Binary Trees with 2 n- 1 Chips",

abstract = "We study labeled chip-firing on binary trees starting with 2n-1 chips initially placed at the root. We prove a sorting property of terminal configurations of the process. We also analyze the end game moves poset and prove that this poset is a modular lattice.",

keywords = "Binary tree, Confluence, Labeled chip-firing, Lattice poset",

author = "Gregg Musiker and Son Nguyen",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive licence to Springer Nature Switzerland AG 2023.",

year = "2024",

month = dec,

doi = "10.1007/s00026-023-00680-0",

language = "English (US)",

volume = "28",

pages = "1167--1197",

journal = "Annals of Combinatorics",

issn = "0218-0006",

publisher = "Birkhauser Verlag Basel",

number = "4",

}

TY - JOUR

T1 - Labeled Chip-Firing on Binary Trees with 2 n- 1 Chips

AU - Musiker, Gregg

AU - Nguyen, Son

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2023.

PY - 2024/12

Y1 - 2024/12

N2 - We study labeled chip-firing on binary trees starting with 2n-1 chips initially placed at the root. We prove a sorting property of terminal configurations of the process. We also analyze the end game moves poset and prove that this poset is a modular lattice.

AB - We study labeled chip-firing on binary trees starting with 2n-1 chips initially placed at the root. We prove a sorting property of terminal configurations of the process. We also analyze the end game moves poset and prove that this poset is a modular lattice.

KW - Binary tree

KW - Confluence

KW - Labeled chip-firing

KW - Lattice poset

UR - http://www.scopus.com/inward/record.url?scp=85179739066&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85179739066&partnerID=8YFLogxK

U2 - 10.1007/s00026-023-00680-0

DO - 10.1007/s00026-023-00680-0

M3 - Article

AN - SCOPUS:85179739066

SN - 0218-0006

VL - 28

SP - 1167

EP - 1197

JO - Annals of Combinatorics

JF - Annals of Combinatorics

IS - 4

ER -