The Computational Complexity of Rules for the Character Table of S_n
摘要
The Murnaghan-Nakayama rule is the classical formula for computing the character table of S_n. Y. Roichman has recently discovered a rule for the Kazhdan-Lusztig characters of q-Hecke algebras of type A, which can also be used for the character table of S_n. For each of the two rules, we give an algorithm for computing entries in the character table of S_n. We then analyze the computational complexity of the two algorithms, and in the case of characters indexed by partitions in the (k,l)-hook, compare their complexities to each other. It turns out that the algorithm based on the Murnaghan-Nakayama rule requires far less operations than the other algorithm. We note the algorithms' complexities' relation to two enumeration problems of Young diagrams and Young tableaux.
引用
@article{arxiv.math/0309225,
title = {The Computational Complexity of Rules for the Character Table of S_n},
author = {Dan Bernstein},
journal= {arXiv preprint arXiv:math/0309225},
year = {2007}
}
备注
24 pages