From the above lemmas it follows that if we can reach an SRCT [[tau].
Let [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] be the C-linear span of SRCTs that are greater than or equal to an SRCT [[tau].
alpha]], where [alpha] is the shape of the SRCT [[tau].
An SRCT [tau] of shape [alpha] is said to be a source tableau if it satisfies the condition that for every i [not member of] Des([tau]) and satisfying i [not equal to] n, we have that i + 1 lies to the immediate left of i.
1] [member of] SRCT([alpha]) is a source tableau if and only if there does not exist an SRCT [[tau].
Recall that given any composition [alpha], we denote the unique SRCT of shape [alpha] and descent composition a by [[tau].
alpha]] is cyclically generated by a single SRCT, termed tableau-cyclic, and use this to classify all compositions [alpha] [?
less than or equal to]i] denote the SRCT comprising of all cells whose entries are [less than or equal to] i.
0], and denote the set of all SRCTs of shape [[alpha].
In order to define an action on SRCTs we first need the concept of attacking.
We will use these operators to define a new partial order on SRCTs of the same shape.
Let [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] denote the C-linear span of all SRCTs in [E.
