A q-Analog of Foulke's conjecture

François Bergeron

A q-Analog of Foulke's conjecture

Combinatorics 2016-07-04 v4 Representation Theory

Authors: François Bergeron

Abstract

We propose a $q$ -analog of classical plethystic conjectures due to Foulkes. In our conjectures, a divided difference of plethysms of Hall-Littlewood polynomials $H_n(\mathbf{x};q)$ replaces the analogous difference of plethysms of complete homogeneous symmetric functions $h_n(\mathbf{x})$ 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.

Keywords

q-analog foulkes conjecture plethysm hall-littlewood polynomials symmetric functions complete homogeneous symmetric functions combinatorial conjectures

Cite

@article{arxiv.1602.08134,
  title  = {A q-Analog of Foulke's conjecture},
  author = {François Bergeron},
  journal= {arXiv preprint arXiv:1602.08134},
  year   = {2016}
}

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13 pages

A q-Analog of Foulke's conjecture

Abstract

Keywords

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