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arXiv · 1512.05319

On the Complexity of Multiplication in the Iwahori--Hecke Algebra of the Symmetric Group

Alice C. Niemeyer·Götz Pfeiffer·Cheryl E. Praeger
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Abstract

We present new efficient data structures for elements of Coxeter groups of type $A_m$ and their associated Iwahori--Hecke algebras $H(A_m)$. Usually, elements of $H(A_m)$ are represented as simple coefficient list of length $M = (m+1)!$ with respect to the standard basis, indexed by the elements of the Coxeter group. In the new data structure, elements of $H(A_m)$ are represented as nested coefficient lists. While the cost of addition is the same in both data structures, the new data structure leads to a huge improvement in the cost of multiplication in~$H(A_m)$.

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Alice C. Niemeyer, Götz Pfeiffer, Cheryl E. Praeger. 2016-08-30. On the Complexity of Multiplication in the Iwahori--Hecke Algebra of the Symmetric Group. https://doi.org/10.1016/j.jsc.2016.09.001

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