0,9

A conugacy class of the symmetric group S_n with the cycle structure given by the partition, listed in the A-St order, consists of even, resp. odd, permutations if a(n,m) is even, resp. odd.

See A115198 for the parity of a(n,m) with 1 for even, 0 for odd (main entry).

See A115199 for the parity of a(n,m) with 0 for even, 1 for odd.

The parity of these numbers determines whether a conjugacy class of the symmetric group S_n, which is determined by its cycle structure, consists of even or odd permutations.

The row length sequence of this triangle is p(n)=A000041(n) (number of partitions).

W. Lang: First 10 rows.

a(n,m)= sum(e(n,m,2*j),j=1..floor(n/2)) with the exponents e(n,m,k) of the m-th partition of n in the A-St order; i.e. the sum of the exponents of the even parts of the partition (1^e(n,m,1),2^e(n,m,2),..., n^e(n,m,n)).

[0];[1, 0];[0, 1, 0];[1, 0, 2, 1, 0];[0, 1, 1, 0, 2, 1, 0];...

The sequence of row lengths is A066898 (total number of even parts in all partitions of n.

Sequence in context: A035227 A049340 A056929 this_sequence A118229 A117201 A060953

Adjacent sequences: A115198 A115199 A115200 this_sequence A115202 A115203 A115204

nonn,easy,tabf

Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Feb 23 2006