Geodesic
A \(q\)-analog of Foulkes' conjecture
François Bergeron1
1Université du Québec à Montréal
The electronic journal of combinatorics, Tome 24 (2017) no. 1
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We propose a $q$-analog of classical plethystic conjectures due to Foulkes. In our conjectures, a divided difference of plethysms of Hall-Littlewood polynomials $H_n(\boldsymbol{x};q)$ replaces the analogous difference of plethysms of complete homogeneous symmetric functions $h_n(\boldsymbol{x})$ in Foulkes' conjecture. At $q=0$, we get back the original statement of Foulkes, and we show that our version holds at $q=1$. We discuss further supporting evidence, as well as various generalizations, including a $(q,t)$-version.
DOI : 10.37236/6004
Classification : 05A30, 05E05
Mots-clés : Foulkes conjecture, Macdonald polynomials, \(q\)-analog

François Bergeron  1

1 Université du Québec à Montréal 
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     author = {Fran\c{c}ois Bergeron},
     title = {A \(q\)-analog of {Foulkes'} conjecture},
     journal = {The electronic journal of combinatorics},
     year = {2017},
     volume = {24},
     number = {1},
     doi = {10.37236/6004},
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François Bergeron. A \(q\)-analog of Foulkes' conjecture. The electronic journal of combinatorics, Tome 24 (2017) no. 1. doi: 10.37236/6004

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