Chennai Mathematical Institute

Seminars




2.00 pm, Seminar Hall
Alternating Sign Matrices(ASMs)

Nimisha Pahuja
IISc, Bengaluru.
18-04-18


Abstract

ASMs are a class of square matrices in combinatorics. The formula enumerating all $n\times n$ ASMs was conjectured in 1983 and it took nearly two decades to find a bijective proof for the identity. David Bressoud, in his book "Proofs and Confirmations" recounts the dramatic search for and discovery of the proof. In this talk which summarises Bressoud's book, I will go over the story of the 'ASM conjecture' while explaining the proof briefly and will discuss few of the many objects like plane partitions, fully packed loops, etc which are in bijection with ASMs. Further, I will give some of their applications. This talk is accessible to students the only prerequisites are basic linear algebra and some Idea about bijective proofs and recursions.





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