【摘 要】
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The permutation group (S)n, signed permutation group Bn and even-signed permutation group Dn are known as the Coxeter groups of type A, B and D, respectively.On
【机 构】
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DepartmentofMathematics,NationalTaiwanNormalUniversity
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The permutation group (S)n, signed permutation group Bn and even-signed permutation group Dn are known as the Coxeter groups of type A, B and D, respectively.On (S)n, Bn, Dn Petersen [2] respectively defined the sorting indices sorA, sorB,sorD and proved that they are Mahonian statistics (i.e., equidistributed with the corresponding length function lA,lB or lD).Recently, Chen et al.[1] extended Petersens work to a series of joint equidistributed set-valued statistics, while Poznanovi(c) [3] showed further that the above results hold on a Ferrers board.For (S)n, for instance,(lA, Rmil, Lmap, Lmal) and (sorA, Cyc, Lmap, Lmal) have the same joint distribution over the permutations corresponding to arrangements of n non-attacking rooks on a fixed Ferrers board with n rows and n columns.
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