ABHYANKAR 82nd BIRTHDAY CONFERENCE
SPEAKER: Dr. Sanju Vaidya (Joshi)
TITLE: Applications of Young Tableaux To 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 e xpressions in many diseases such as cancer and
diabetics. 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. We will associate Young Tableaux to
permutations corresponding to the data points of mic roarray curves
using the Robinson-Schensted-Knuth procedure. We will compute the bound
of Ahnert et al corresponding to the map which gives the length of the
longest increasing or decreasing subsequence of a permutation. It may be
noted that Abhyankar-Joshi established many correspondences between
multitableaux and multimonomials by generalizing the
Robinson-Schensted-Knuth procedure in various ways and proved that the
Straightening law of Doubleit-Rota-Stein is not valid in the case of
higher dimensional matrices.