Young Tableaux for Gene Expressions

Abstract

Young tableaux are certain tabular
arrangements of integers. Alfred Young introduced
them to describe irreducible representations of the
symmetric group at the end of the 19th century. We will
use combinatorial algorithms of permutations and
Young tableaux to describe a modification of the
research method of Ahnert et al for identifying
significant genes in the biological processes studied in
microarray experiments. In the last decade, DNA
microarrays (DNA chips) have been used to study gene
expressions in many diseases such as cancer and
diabetes. To analyze data of microarray expression
curves of genes, Ahnert et al associated permutations to
the data points of the microarray curves. Using Monte-
Carlo simulation they established bounds
corresponding to various maps of permutations for any
microarray curve’s algorithmic compressibility which
measures its significance in the underlying biological
process. Using the Robinson- Schensted-Knuth
procedure, we will associate Young tableaux to
permutations corresponding to the data points of
microarray curves. We will calculate the bound of
Ahnert et al corresponding to the map which gives the
length of the longest increasing or decreasing
subsequence of a permutation.