Cell transfer and monomial positivity

Details Cell transfer and monomial positivity Cell transfer and monomial positivity

2005-05-12

arxiv.org/abs/math/0505273v2

Mathematics

Combinatorics

14 pages, 5 figures; final version

Scientific paper

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 $(P,\omega)$-partitions.

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