The combinatorics of symmetric functions and permutation enumeration of the hyperoctahedral group

被引:7
作者
Beck, DA [1 ]
机构
[1] UNIV CALIF SAN DIEGO,DEPT MATH,LA JOLLA,CA 92093
关键词
D O I
10.1016/0012-365X(95)00326-R
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We study permutation enumeration of the hyperoctahedral group B-n through a combinatorial use of the B-n-analogues of symmetric functions, denoted Lambda(B). We define an appropriate homomorphism zeta:Lambda(B) --> Q[x] and remarkably, applying this homomorphism to one of the bases of Lambda(B) produces polynomials which correspond to enumerating B-n with respect to descents. Applying zeta to a second basis corresponds to enumerating a conjugacy class of B-n with respect to a new descent type statistic which arises naturally.
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页码:13 / 45
页数:33
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