Geodesic
Involutions on standard Young tableaux and divisors on metric graphs
Rohit Agrawal1 ; Gregg Musiker1 ; Vladimir Sotirov2 ; Fan Wei3
1University of Minnesota
2University of Wisconsin
3Massachusetts Institute of Technology
The electronic journal of combinatorics, Tome 20 (2013) no. 3
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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 $v_0$-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.
DOI : 10.37236/2590
Classification : 05E10, 05C57, 06A07, 14N10
Mots-clés : metric graphs, tropical geometry, divisors on graphs, chip-firing, Young tableaux, evacuation

Rohit Agrawal  1   ; Gregg Musiker  1   ; Vladimir Sotirov  2   ; Fan Wei  3

1 University of Minnesota
2 University of Wisconsin
3 Massachusetts Institute of Technology 
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     title = {Involutions on standard {Young} tableaux and divisors on metric graphs},
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Rohit Agrawal; Gregg Musiker; Vladimir Sotirov; Fan Wei. Involutions on standard Young tableaux and divisors on metric graphs. The electronic journal of combinatorics, Tome 20 (2013) no. 3. doi: 10.37236/2590

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