Geodesic
\(K\)-Knuth equivalence for increasing tableaux
Christian Gaetz1 ; Michelle Mastrianni2 ; Rebecca Patrias1 ; Hailee Peck1 ; Colleen Robichaux3 ; David Schwein4 ; Ka Yu Tam5
1University of Minnesota
2Carleton College
3Louisiana State University
4Brown University
5Stanford University
The electronic journal of combinatorics, Tome 23 (2016) no. 1
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A $K$-theoretic analogue of RSK insertion and the Knuth equivalence relations were introduced by Buch, Kresch, Shimozono, Tamvakis, and Yong (2006) and Buch and Samuel (2013), respectively. The resulting $K$-Knuth equivalence relations on words and increasing tableaux on $[n]$ has prompted investigation into the equivalence classes of tableaux arising from these relations. Of particular interest are the tableaux that are unique in their class, which we refer to as unique rectification targets (URTs). In this paper, we give several new families of URTs and a bound on the length of intermediate words connecting two $K$-Knuth equivalent words. In addition, we describe an algorithm to determine if two words are $K$-Knuth equivalent and to compute all $K$-Knuth equivalence classes of tableaux on $[n]$.
DOI : 10.37236/4805
Classification : 05E10
Mots-clés : increasing tableaux, \(K\)-Knuth equivalence, \(K\)-theory, jeu de taquin

Christian Gaetz  1   ; Michelle Mastrianni  2   ; Rebecca Patrias  1   ; Hailee Peck  1   ; Colleen Robichaux  3   ; David Schwein  4   ; Ka Yu Tam  5

1 University of Minnesota
2 Carleton College
3 Louisiana State University
4 Brown University
5 Stanford University 
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     title = {\(K\)-Knuth equivalence for increasing tableaux},
     journal = {The electronic journal of combinatorics},
     year = {2016},
     volume = {23},
     number = {1},
     doi = {10.37236/4805},
     zbl = {1332.05148},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/4805/}
}
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Christian Gaetz; Michelle Mastrianni; Rebecca Patrias; Hailee Peck; Colleen Robichaux; David Schwein; Ka Yu Tam. \(K\)-Knuth equivalence for increasing tableaux. The electronic journal of combinatorics, Tome 23 (2016) no. 1. doi: 10.37236/4805

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