Abstract
We give combinatorial proofs that certain families of differences of products of Schur functions are monomial-positive. We show in addition that such monomial-positivity is to be expected of a large class of generating functions with combinatorial definitions similar to Schur functions. These generating functions are defined on posets with labelled Hasse diagrams and include for example generating functions of Stanley's (P,ω)-partitions.
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T.L. was supported in part by NSF DMS-0600677.
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Lam, T., Pylyavskyy, P. Cell transfer and monomial positivity. J Algebr Comb 26, 209–224 (2007). https://doi.org/10.1007/s10801-006-0054-z
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DOI: https://doi.org/10.1007/s10801-006-0054-z
Keywords
- Symmetric functions
- Monomial positivity
- P-partitions