Involutions on standard Young tableaux and divisors on metric graphs

Rohit Agrawal; Gregg Musiker; Vladimir Sotirov; Fan Wei

doi:10.37236/2590

Involutions on standard Young tableaux and divisors on metric graphs

Rohit Agrawal, Gregg Musiker, Vladimir Sotirov, Fan Wei

Mathematics

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

3 Scopus citations

Abstract

We elaborate upon a bijection discovered by Cools, Draisma, Payne, and Robeva (2012) between the set of rectangular standard Young tableaux and the set of equivalence classes of chip configurations on certain metric graphs under the relation of linear equivalence. We present an explicit formula for computing the v₀-reduced divisors (representatives of the equivalence classes) associated to given tableaux, and use this formula to prove (i) evacuation of tableaux corresponds (under the bijection) to reflecting the metric graph, and (ii) conjugation of the tableaux corresponds to taking the Riemann-Roch dual of the divisor.

Original language	English (US)
Journal	Electronic Journal of Combinatorics
Volume	20
Issue number	3
DOIs	https://doi.org/10.37236/2590
State	Published - Sep 6 2013

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics
Applied Mathematics

Keywords

Chip-firing
Divisors on graphs
Evacuation
Metric graphs
Tropical geometry
Young tableaux

Access to Document

10.37236/2590

Cite this

@article{d5ef1f50e3db429eb05e68b47a28be56,

title = "Involutions on standard Young tableaux and divisors on metric graphs",

abstract = "We elaborate upon a bijection discovered by Cools, Draisma, Payne, and Robeva (2012) between the set of rectangular standard Young tableaux and the set of equivalence classes of chip configurations on certain metric graphs under the relation of linear equivalence. We present an explicit formula for computing the v0-reduced divisors (representatives of the equivalence classes) associated to given tableaux, and use this formula to prove (i) evacuation of tableaux corresponds (under the bijection) to reflecting the metric graph, and (ii) conjugation of the tableaux corresponds to taking the Riemann-Roch dual of the divisor.",

keywords = "Chip-firing, Divisors on graphs, Evacuation, Metric graphs, Tropical geometry, Young tableaux",

author = "Rohit Agrawal and Gregg Musiker and Vladimir Sotirov and Fan Wei",

year = "2013",

month = sep,

day = "6",

doi = "10.37236/2590",

language = "English (US)",

volume = "20",

journal = "Electronic Journal of Combinatorics",

issn = "1077-8926",

publisher = "Electronic Journal of Combinatorics",

number = "3",

}

TY - JOUR

T1 - Involutions on standard Young tableaux and divisors on metric graphs

AU - Agrawal, Rohit

AU - Musiker, Gregg

AU - Sotirov, Vladimir

AU - Wei, Fan

PY - 2013/9/6

Y1 - 2013/9/6

N2 - We elaborate upon a bijection discovered by Cools, Draisma, Payne, and Robeva (2012) between the set of rectangular standard Young tableaux and the set of equivalence classes of chip configurations on certain metric graphs under the relation of linear equivalence. We present an explicit formula for computing the v0-reduced divisors (representatives of the equivalence classes) associated to given tableaux, and use this formula to prove (i) evacuation of tableaux corresponds (under the bijection) to reflecting the metric graph, and (ii) conjugation of the tableaux corresponds to taking the Riemann-Roch dual of the divisor.

AB - We elaborate upon a bijection discovered by Cools, Draisma, Payne, and Robeva (2012) between the set of rectangular standard Young tableaux and the set of equivalence classes of chip configurations on certain metric graphs under the relation of linear equivalence. We present an explicit formula for computing the v0-reduced divisors (representatives of the equivalence classes) associated to given tableaux, and use this formula to prove (i) evacuation of tableaux corresponds (under the bijection) to reflecting the metric graph, and (ii) conjugation of the tableaux corresponds to taking the Riemann-Roch dual of the divisor.

KW - Chip-firing

KW - Divisors on graphs

KW - Evacuation

KW - Metric graphs

KW - Tropical geometry

KW - Young tableaux

UR - http://www.scopus.com/inward/record.url?scp=84884164640&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84884164640&partnerID=8YFLogxK

U2 - 10.37236/2590

DO - 10.37236/2590

M3 - Article

AN - SCOPUS:84884164640

SN - 1077-8926

VL - 20

JO - Electronic Journal of Combinatorics

JF - Electronic Journal of Combinatorics

IS - 3

ER -

Involutions on standard Young tableaux and divisors on metric graphs

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

Other files and links

Fingerprint

Cite this