Á. Gutiérrez and
Christian Krattenthaler
Schur log-concavity and the quantum Pascal triangle
(14 pages)
Abstract.
We say a sequence f0, f1, f2, ... of symmetric functions is Schur
log-concave if fn2
- fn-1fn+1
is Schur positive for all n≥1. We
conjecture that a vast number of sequences of Schur functions
satisfies this property, and show it for sequences of Schur functions indexed
by partitions with a growing first part. Our findings are related to work of
Lam, Postnikov and Pylyavskyy on Schur positivity,
and of Butler, Sagan, and the second author on q-log-concavity.
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