Cell transfer and monomial positivity

Thomas Lam; Pavlo Pylyavskyy

doi:10.1007/s10801-006-0054-z

Cell transfer and monomial positivity

Thomas Lam, Pavlo Pylyavskyy

School of Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

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.

Original language	English (US)
Pages (from-to)	209-224
Number of pages	16
Journal	Journal of Algebraic Combinatorics
Volume	26
Issue number	2
DOIs	https://doi.org/10.1007/s10801-006-0054-z
State	Published - Sep 2007

Bibliographical note

Funding Information:
T.L. was supported in part by NSF DMS-0600677.

Keywords

Monomial positivity
P-partitions
Symmetric functions

Publisher link

10.1007/s10801-006-0054-z

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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.",

keywords = "Monomial positivity, P-partitions, Symmetric functions",

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AB - 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.

KW - Monomial positivity

KW - P-partitions

KW - Symmetric functions

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Cell transfer and monomial positivity

Abstract

Bibliographical note

Keywords

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