A combinatorial approach to the power of 2 in the number of involutions

Jang Soo Kim (김장수)

Dept. of Mathematical Sciences, KAIST, Korea.

Dept. of Mathematical Sciences, KAIST, Korea.

2008/12/11 Thu, 5:30PM-6:30PM

We prove combinatorially that the largest power of 2 in the number of involutions of length n is equal to [n/2]-2[n/4] +[(n+1)/4]. We show that the smallest period of the sequence of odd factors in the number of involutions modulo 2

^{s}is 2^{s+1}for s>2. We also consider the largest power of 2 in the number of even and odd involutions.Tags: 김장수