TY - JOUR
T1 - Mixing and Covering in the Symmetric Groups
AU - Vishne, Uzi
PY - 1998/7/1
Y1 - 1998/7/1
N2 - We discuss mixing and covering theorems in the symmetric groups. We present an example of a covering without mixing, and study the conjugacy class [2n/2] of symmetric groupSn, which demonstrates mixing without covering. We derive some new character identities from the computation of [2n/2]2, and also compute [2n/2]3, filling a hole between theorems of J. L. Brenner (J. Austral. Math. Soc. Ser. A25,1978, 210-214) and Y. Dvir (in"Products of Conjugacy Classes in Groups," Lecture Notes in Math., Vol. 1112, Springer-Verlag, New York/Berlin, 1985). This computation also motivates a certain classification of 3-colored 3-regular graphs.
AB - We discuss mixing and covering theorems in the symmetric groups. We present an example of a covering without mixing, and study the conjugacy class [2n/2] of symmetric groupSn, which demonstrates mixing without covering. We derive some new character identities from the computation of [2n/2]2, and also compute [2n/2]3, filling a hole between theorems of J. L. Brenner (J. Austral. Math. Soc. Ser. A25,1978, 210-214) and Y. Dvir (in"Products of Conjugacy Classes in Groups," Lecture Notes in Math., Vol. 1112, Springer-Verlag, New York/Berlin, 1985). This computation also motivates a certain classification of 3-colored 3-regular graphs.
UR - http://www.scopus.com/inward/record.url?scp=0040005753&partnerID=8YFLogxK
U2 - 10.1006/jabr.1997.7366
DO - 10.1006/jabr.1997.7366
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AN - SCOPUS:0040005753
SN - 0021-8693
VL - 205
SP - 119
EP - 140
JO - Journal of Algebra
JF - Journal of Algebra
IS - 1
ER -