STRAIGHTENING RULE FOR AN m#-TRUNCATED POLYNOMIAL RING
KAY JIN LIM
Abstract. We consider a certain quotient of a polynomial ring categorified by 
both the isomorphic Green rings of symmetric group and Schur algebra generated 
by the signed Young permutation modules and mixed powers respectively. They 
have bases parametrised by pairs of partitions whose second partitions are mul- 
tiple of the odd prime p the characteristic of the underlying field. We provide 
an explicit formula rewriting a signed Young permutation module (respectively, 
mixed power) in terms of signed Young permutation modules (respectively, mixed 
powers) labelled by those pair of partitions. As a result, the combinatorial num- 
ber, for each partition, the number of compositions which can be rearranged to 
the partition and whose all partial sums are not divisible by p arises naturally.