1Department of Mathematics Louisiana State University Baton Rouge, LA 70803 2Department of Mathematics and Statistics University of North Carolina Greensboro Greensboro, NC 27402
The electronic journal of combinatorics, Tome 20 (2013) no. 3
We prove generalized arithmetic-geometric mean inequalities for quasi-means arising from symmetric polynomials. The inequalities are satisfied by all positive, homogeneous symmetric polynomials, as well as a certain family of non-homogeneous polynomials; this family allows us to prove the following combinatorial result for marked square grids.Suppose that the cells of a $n \times n$ checkerboard are each independently filled or empty, where the probability that a cell is filled depends only on its column. We prove that for any $0 \leq \ell \leq n$, the probability that each column has at most $\ell$ filled sites is less than or equal to the probability that each row has at most $\ell$ filled sites.
1
Department of Mathematics
Louisiana State University
Baton Rouge, LA 70803
2
Department of Mathematics and Statistics University of North Carolina Greensboro Greensboro, NC 27402
@article{10_37236_2915,
author = {Karl Mahlburg and Clifford Smyth},
title = {Symmetric polynomials and symmetric mean inequalities},
journal = {The electronic journal of combinatorics},
year = {2013},
volume = {20},
number = {3},
doi = {10.37236/2915},
zbl = {1295.05262},
url = {http://geodesic.mathdoc.fr/articles/10.37236/2915/}
}
TY - JOUR
AU - Karl Mahlburg
AU - Clifford Smyth
TI - Symmetric polynomials and symmetric mean inequalities
JO - The electronic journal of combinatorics
PY - 2013
VL - 20
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/2915/
DO - 10.37236/2915
ID - 10_37236_2915
ER -
%0 Journal Article
%A Karl Mahlburg
%A Clifford Smyth
%T Symmetric polynomials and symmetric mean inequalities
%J The electronic journal of combinatorics
%D 2013
%V 20
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/2915/
%R 10.37236/2915
%F 10_37236_2915
Karl Mahlburg; Clifford Smyth. Symmetric polynomials and symmetric mean inequalities. The electronic journal of combinatorics, Tome 20 (2013) no. 3. doi: 10.37236/2915
