Abstract
We prove an inequality between three measures of disorder on the symmetric group on n elements. This inequality has been inspired by the well-known Diaconis-Graham inequalities. We also discuss when the inequality is satisfied as equality, and how often this happens. In the case n is odd, the number of permutations that satisfy the equality is a simple function of the Lucas numbers. In addition, we show that a quantity involved in the new inequality (which is a function of the three measures of disorder) can be used to give a new characterization of the dihedral group.
Original language | English |
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Pages (from-to) | 226-245 |
Number of pages | 20 |
Journal | Australasian Journal of Combinatorics |
Volume | 63 |
Issue number | 2 |
State | Published - Sep 21 2015 |