Check the equation for the cycle index of S4.
Verify the details of locally finite partial orders.
Evaluate the cycle indicator polynomial of the action of the
group Cp´Cp´Cp, p being an odd prime, on itself by left
multiplication. Evaluate also the cycle indicator polynomial of the action of
nonabelian group of order p3 on itself by left multiplication.
Express the cycle indicator C(Sn ,n) in terms of the polynomials
C(Sk,k), 1 <= k <= n.
Check that addition and convolution in fact define a ring structure on the
set IF(P) of incidence functions.
Let (L,Ù,Ú) denote a lattice and (L, <= ) the corresponding
poset. We call fÎIF(L) multiplicative if and only if,
x,y in L, an order isomorphism
[xÙy,xÚy] simeq [xÙy,x]´[xÙy,y]
Prove the details in the examples.
Evaluate the characters of the natural actions of SX on
Xn and on Xni.
last changed: August 28, 2001