Recent developments in algebraic combinatorics

Recent Developments in Algebraic Combinatorics

We survey three recent developments in algebraic combinatorics. The first is the theory of cluster algebras and the Laurent phenomenon of Sergey Fomin and Andrei Zelevinsky. The second is the construction of toric Schur functions and their application to computing three-point Gromov-Witten invariants, by Alexander Postnikov. The third development is the construction of intersection cohomology f...

Recent Progress in Algebraic Combinatorics

We survey three recent breakthroughs in algebraic combinatorics. The first is the proof by Knutson and Tao, and later Derksen and Weyman, of the saturation conjecture for Littlewood-Richardson coefficients. The second is the proof of the n! and (n + 1)n−1 conjectures by Haiman. The final breakthrough is the determination by Baik, Deift, and Johansson of the limiting behavior of the length of th...

Recent Progress in Algebraic Combinatorics

Recent Advances in Algebraic and Enumerative Combinatorics

Algebraic and enumerative combinatorics is concerned with objects that have both a combinatorial and an algebraic interpretation. It is a highly active area of the mathematical sciences, with many connections and applications to other areas, including algebraic geometry, representation theory, topology, mathematical physics and statistical mechanics. Enumerative questions arise in the mathemati...

Phytoestrogens: recent developments

Phytoestrogens are polyphenolic non-steroidal plant compounds with estrogen like activity exerted through estrogen receptors. These receptors are distributed in several tissues such as male and female reproductive systems, bones, cardiovascular and central nervous systems. These natural phenolic compounds include isoflavonoids, flavonoids, lignans and stilbenes. Isoflavonoids are the most studi...