Rowmotion and Echelonmotion Article Swipe

PDF

Colin Defant , Yuhan Jiang , René Marczinzik , Adrien Segovia , David E Speyer , Hugh Thomas , Nathan Williams ·

YOU? · · 2025 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2507.18230

Given a linear extension $σ$ of a finite poset $R$, we consider the permutation matrix indexing the Schubert cell containing the Cartan matrix of $R$ with respect to $σ$. This yields a bijection $\mathrm{Ech}_σ\colon R\to R$ that we call echelonmotion; it is the inverse of the Coxeter permutation studied by Klász, Marczinzik, and Thomas. Those authors proved that echelonmotion agrees with rowmotion when $R$ is a distributive lattice. We generalize this result to semidistributive lattices. In addition, we prove that every trim lattice has a linear extension with respect to which echelonmotion agrees with rowmotion. We also show that echelonmotion on an Eulerian poset (with respect to any linear extension) is an involution. Finally, we initiate the study of echelon-independent posets, which are posets for which echelonmotion is independent of the chosen linear extension. We prove that a lattice is echelon-independent if and only if it is semidistributive. Moreover, we show that echelon-independent connected posets are bounded and have semidistributive MacNeille completions.

Related Topics

Elizabeth (Given Name)

Jack (Given Name)

Concepts

No concepts available.

Metadata

Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2507.18230
PDF: https://arxiv.org/pdf/2507.18230
OA Status: green
OpenAlex ID: https://openalex.org/W4415233467

All OpenAlex metadata

Raw OpenAlex JSON

OpenAlex ID: https://openalex.org/W4415233467

Canonical identifier for this work in OpenAlex
DOI: https://doi.org/10.48550/arxiv.2507.18230

Digital Object Identifier
Title: Rowmotion and Echelonmotion

Work title
Type: preprint

OpenAlex work type
Language: en

Primary language
Publication year: 2025

Year of publication
Publication date: 2025-07-24

Full publication date if available
Authors: Colin Defant, Yuhan Jiang, René Marczinzik, Adrien Segovia, David E Speyer, Hugh Thomas, Nathan Williams

List of authors in order
Landing page: https://arxiv.org/abs/2507.18230

Publisher landing page
PDF URL: https://arxiv.org/pdf/2507.18230

Direct link to full text PDF
Open access: Yes

Whether a free full text is available
OA status: green

Open access status per OpenAlex
OA URL: https://arxiv.org/pdf/2507.18230

Direct OA link when available
Cited by: 0

Total citation count in OpenAlex

Full payload

id	https://openalex.org/W4415233467
doi	https://doi.org/10.48550/arxiv.2507.18230
ids.doi	https://doi.org/10.48550/arxiv.2507.18230
ids.openalex	https://openalex.org/W4415233467
fwci
type	preprint
title	Rowmotion and Echelonmotion
biblio.issue
biblio.volume
biblio.last_page
biblio.first_page
topics[0].id	https://openalex.org/T11246
topics[0].field.id	https://openalex.org/fields/27
topics[0].field.display_name	Medicine
topics[0].score	0.9265999794006348
topics[0].domain.id	https://openalex.org/domains/4
topics[0].domain.display_name	Health Sciences
topics[0].subfield.id	https://openalex.org/subfields/2732
topics[0].subfield.display_name	Orthopedics and Sports Medicine
topics[0].display_name	Sports injuries and prevention
topics[1].id	https://openalex.org/T12252
topics[1].field.id	https://openalex.org/fields/22
topics[1].field.display_name	Engineering
topics[1].score	0.9021999835968018
topics[1].domain.id	https://openalex.org/domains/3
topics[1].domain.display_name	Physical Sciences
topics[1].subfield.id	https://openalex.org/subfields/2211
topics[1].subfield.display_name	Mechanics of Materials
topics[1].display_name	Mechanical stress and fatigue analysis
is_xpac	False
apc_list
apc_paid
language	en
locations[0].id	pmh:oai:arXiv.org:2507.18230
locations[0].is_oa	True
locations[0].source.id	https://openalex.org/S4306400194
locations[0].source.issn
locations[0].source.type	repository
locations[0].source.is_oa	True
locations[0].source.issn_l
locations[0].source.is_core	False
locations[0].source.is_in_doaj	False
locations[0].source.display_name	arXiv (Cornell University)
locations[0].source.host_organization	https://openalex.org/I205783295
locations[0].source.host_organization_name	Cornell University
locations[0].source.host_organization_lineage	https://openalex.org/I205783295
locations[0].license
locations[0].pdf_url	https://arxiv.org/pdf/2507.18230
locations[0].version	submittedVersion
locations[0].raw_type	text
locations[0].license_id
locations[0].is_accepted	False
locations[0].is_published	False
locations[0].raw_source_name
locations[0].landing_page_url	http://arxiv.org/abs/2507.18230
locations[1].id	doi:10.48550/arxiv.2507.18230
locations[1].is_oa	True
locations[1].source.id	https://openalex.org/S4306400194
locations[1].source.issn
locations[1].source.type	repository
locations[1].source.is_oa	True
locations[1].source.issn_l
locations[1].source.is_core	False
locations[1].source.is_in_doaj	False
locations[1].source.display_name	arXiv (Cornell University)
locations[1].source.host_organization	https://openalex.org/I205783295
locations[1].source.host_organization_name	Cornell University
locations[1].source.host_organization_lineage	https://openalex.org/I205783295
locations[1].license
locations[1].pdf_url
locations[1].version
locations[1].raw_type	article
locations[1].license_id
locations[1].is_accepted	False
locations[1].is_published
locations[1].raw_source_name
locations[1].landing_page_url	https://doi.org/10.48550/arxiv.2507.18230
indexed_in	arxiv, datacite
authorships[0].author.id	https://openalex.org/A5050123780
authorships[0].author.orcid	https://orcid.org/0000-0002-4910-5765
authorships[0].author.display_name	Colin Defant
authorships[0].author_position	first
authorships[0].raw_author_name	Defant, Colin
authorships[0].is_corresponding	False
authorships[1].author.id	https://openalex.org/A5120018633
authorships[1].author.orcid
authorships[1].author.display_name	Yuhan Jiang
authorships[1].author_position	middle
authorships[1].raw_author_name	Jiang, Yuhan
authorships[1].is_corresponding	False
authorships[2].author.id	https://openalex.org/A5004747002
authorships[2].author.orcid	https://orcid.org/0000-0003-3380-0453
authorships[2].author.display_name	René Marczinzik
authorships[2].author_position	middle
authorships[2].raw_author_name	Marczinzik, Rene
authorships[2].is_corresponding	False
authorships[3].author.id	https://openalex.org/A5006273528
authorships[3].author.orcid
authorships[3].author.display_name	Adrien Segovia
authorships[3].author_position	middle
authorships[3].raw_author_name	Segovia, Adrien
authorships[3].is_corresponding	False
authorships[4].author.id	https://openalex.org/A5021128761
authorships[4].author.orcid	https://orcid.org/0000-0003-4540-2559
authorships[4].author.display_name	David E Speyer
authorships[4].author_position	middle
authorships[4].raw_author_name	Speyer, David E
authorships[4].is_corresponding	False
authorships[5].author.id	https://openalex.org/A5103229024
authorships[5].author.orcid	https://orcid.org/0000-0002-3643-7189
authorships[5].author.display_name	Hugh Thomas
authorships[5].author_position	middle
authorships[5].raw_author_name	Thomas, Hugh
authorships[5].is_corresponding	False
authorships[6].author.id	https://openalex.org/A5034861890
authorships[6].author.orcid	https://orcid.org/0000-0003-2084-6428
authorships[6].author.display_name	Nathan Williams
authorships[6].author_position	last
authorships[6].raw_author_name	Williams, Nathan
authorships[6].is_corresponding	False
has_content.pdf	False
has_content.grobid_xml	False
is_paratext	False
open_access.is_oa	True
open_access.oa_url	https://arxiv.org/pdf/2507.18230
open_access.oa_status	green
open_access.any_repository_has_fulltext	False
created_date	2025-10-16T00:00:00
display_name	Rowmotion and Echelonmotion
has_fulltext	False
is_retracted	False
updated_date	2025-11-06T06:51:31.235846
primary_topic.id	https://openalex.org/T11246
primary_topic.field.id	https://openalex.org/fields/27
primary_topic.field.display_name	Medicine
primary_topic.score	0.9265999794006348
primary_topic.domain.id	https://openalex.org/domains/4
primary_topic.domain.display_name	Health Sciences
primary_topic.subfield.id	https://openalex.org/subfields/2732
primary_topic.subfield.display_name	Orthopedics and Sports Medicine
primary_topic.display_name	Sports injuries and prevention
cited_by_count	0
locations_count	2
best_oa_location.id	pmh:oai:arXiv.org:2507.18230
best_oa_location.is_oa	True
best_oa_location.source.id	https://openalex.org/S4306400194
best_oa_location.source.issn
best_oa_location.source.type	repository
best_oa_location.source.is_oa	True
best_oa_location.source.issn_l
best_oa_location.source.is_core	False
best_oa_location.source.is_in_doaj	False
best_oa_location.source.display_name	arXiv (Cornell University)
best_oa_location.source.host_organization	https://openalex.org/I205783295
best_oa_location.source.host_organization_name	Cornell University
best_oa_location.source.host_organization_lineage	https://openalex.org/I205783295
best_oa_location.license
best_oa_location.pdf_url	https://arxiv.org/pdf/2507.18230
best_oa_location.version	submittedVersion
best_oa_location.raw_type	text
best_oa_location.license_id
best_oa_location.is_accepted	False
best_oa_location.is_published	False
best_oa_location.raw_source_name
best_oa_location.landing_page_url	http://arxiv.org/abs/2507.18230
primary_location.id	pmh:oai:arXiv.org:2507.18230
primary_location.is_oa	True
primary_location.source.id	https://openalex.org/S4306400194
primary_location.source.issn
primary_location.source.type	repository
primary_location.source.is_oa	True
primary_location.source.issn_l
primary_location.source.is_core	False
primary_location.source.is_in_doaj	False
primary_location.source.display_name	arXiv (Cornell University)
primary_location.source.host_organization	https://openalex.org/I205783295
primary_location.source.host_organization_name	Cornell University
primary_location.source.host_organization_lineage	https://openalex.org/I205783295
primary_location.license
primary_location.pdf_url	https://arxiv.org/pdf/2507.18230
primary_location.version	submittedVersion
primary_location.raw_type	text
primary_location.license_id
primary_location.is_accepted	False
primary_location.is_published	False
primary_location.raw_source_name
primary_location.landing_page_url	http://arxiv.org/abs/2507.18230
publication_date	2025-07-24
publication_year	2025
referenced_works_count	0
abstract_inverted_index.a	1, 6, 31, 65, 84, 137
abstract_inverted_index.In	75
abstract_inverted_index.R$	35
abstract_inverted_index.We	68, 95, 134
abstract_inverted_index.an	101, 111
abstract_inverted_index.by	49
abstract_inverted_index.if	141, 144
abstract_inverted_index.is	41, 64, 110, 127, 139, 146
abstract_inverted_index.it	40, 145
abstract_inverted_index.of	5, 23, 44, 118, 129
abstract_inverted_index.on	100
abstract_inverted_index.to	27, 72, 89, 106
abstract_inverted_index.we	10, 37, 77, 114, 149
abstract_inverted_index.$R$	24, 63
abstract_inverted_index.and	52, 142, 157
abstract_inverted_index.any	107
abstract_inverted_index.are	122, 155
abstract_inverted_index.for	124
abstract_inverted_index.has	83
abstract_inverted_index.the	12, 16, 20, 42, 45, 116, 130
abstract_inverted_index.$R$,	9
abstract_inverted_index.$σ$	4
abstract_inverted_index.R\to	34
abstract_inverted_index.This	29
abstract_inverted_index.also	96
abstract_inverted_index.call	38
abstract_inverted_index.cell	18
abstract_inverted_index.have	158
abstract_inverted_index.only	143
abstract_inverted_index.show	97, 150
abstract_inverted_index.that	36, 57, 79, 98, 136, 151
abstract_inverted_index.this	70
abstract_inverted_index.trim	81
abstract_inverted_index.when	62
abstract_inverted_index.with	25, 60, 87, 93
abstract_inverted_index.$σ$.	28
abstract_inverted_index.(with	104
abstract_inverted_index.Given	0
abstract_inverted_index.Those	54
abstract_inverted_index.every	80
abstract_inverted_index.poset	8, 103
abstract_inverted_index.prove	78, 135
abstract_inverted_index.study	117
abstract_inverted_index.which	90, 121, 125
abstract_inverted_index.Cartan	21
abstract_inverted_index.agrees	59, 92
abstract_inverted_index.chosen	131
abstract_inverted_index.finite	7
abstract_inverted_index.linear	2, 85, 108, 132
abstract_inverted_index.matrix	14, 22
abstract_inverted_index.posets	123, 154
abstract_inverted_index.proved	56
abstract_inverted_index.result	71
abstract_inverted_index.yields	30
abstract_inverted_index.Coxeter	46
abstract_inverted_index.Klász,	50
abstract_inverted_index.Thomas.	53
abstract_inverted_index.authors	55
abstract_inverted_index.bounded	156
abstract_inverted_index.inverse	43
abstract_inverted_index.lattice	82, 138
abstract_inverted_index.posets,	120
abstract_inverted_index.respect	26, 88, 105
abstract_inverted_index.studied	48
abstract_inverted_index.Eulerian	102
abstract_inverted_index.Finally,	113
abstract_inverted_index.Schubert	17
abstract_inverted_index.consider	11
abstract_inverted_index.indexing	15
abstract_inverted_index.initiate	115
abstract_inverted_index.lattice.	67
abstract_inverted_index.MacNeille	160
abstract_inverted_index.Moreover,	148
abstract_inverted_index.addition,	76
abstract_inverted_index.bijection	32
abstract_inverted_index.connected	153
abstract_inverted_index.extension	3, 86
abstract_inverted_index.lattices.	74
abstract_inverted_index.rowmotion	61
abstract_inverted_index.containing	19
abstract_inverted_index.extension)	109
abstract_inverted_index.extension.	133
abstract_inverted_index.generalize	69
abstract_inverted_index.rowmotion.	94
abstract_inverted_index.Marczinzik,	51
abstract_inverted_index.independent	128
abstract_inverted_index.involution.	112
abstract_inverted_index.permutation	13, 47
abstract_inverted_index.completions.	161
abstract_inverted_index.distributive	66
abstract_inverted_index.echelonmotion	58, 91, 99, 126
abstract_inverted_index.echelonmotion;	39
abstract_inverted_index.semidistributive	73, 159
abstract_inverted_index.semidistributive.	147
abstract_inverted_index.echelon-independent	119, 140, 152
abstract_inverted_index.$\mathrm{Ech}_σ\colon	33
cited_by_percentile_year
countries_distinct_count	0
institutions_distinct_count	7
citation_normalized_percentile