garnirElement(y,coef,a,b)
garnirElement(y,coef)
garnirElement(y)
A Garnir element is an element which is constructed to remove row descents from a tableau. Given a tableau $T$, the Garnir element is defined for a subset $A$ of the $i$th column and a subset $B$ of the $i+1$ column. It is defined as $ \sum_{\pi} sgn(\pi)\pi(T)$. The $\pi$ are called transversals. They are a set of permutations such that $S_{A \cup B}$ is the disjoint union of $\pi(S_A \times S_B)$.
The identity can always be chosen as a transversal for any pair of sets. Therefore the original tableau $T$ appears along side other tableaux which are closer to being standard. Another property is that this element is equal to zero. Therefore the original polytabloid $e_T$ can be written as $ e_T = \sum_{\pi \neq id} sgn(\pi)\pi(e_T) $
In this implementation the $i$th column is taken to be the parameter b. The set $A$ is all the cells in the $i$th column from the ath row to the bottom. The set $B$ is all the cells in the $i+1$ column from the ath row to the top.
If the number (a,b) are not specified then they are taken as the coordinates of the first row descent of $T$



The object garnirElement is a method function.