Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bumpless Pipedreams, Reduced Word Tableaux and Stanley Symmetric
  Functions   Lam, Lee and Shimozono introduced the structure of bumpless pipedreams in
their study of back stable Schubert calculus. They found that a specific family
of bumpless pipedreams, called EG-pipedreams, can be used to interpret the
Edelman-Greene coefficients appearing in the expansion of a Stanley symmetric
function in the basis of Schur functions. It is well known that the
Edelman-Greene coefficients can also be interpreted in terms of reduced word
tableaux for permutations. Lam, Lee and Shimozono proposed the problem of
finding a shape preserving bijection between reduced word tableaux for a
permutation $w$ and EG-pipedreams of $w$. In this paper, we construct such a
bijection. The key ingredients are two new developed isomorphic tree structures
associated to $w$: the modified Lascoux-Sch\"{u}tzenberger tree of $w$ and the
Edelman-Greene tree of $w$. Using the Little map, we show that the leaves in
the modified Lascoux-Sch\"{u}tzenberger of $w$ are in bijection with the
reduced word tableaux for $w$. On the other hand, applying the droop operation
on bumpless pipedreams also introduced by Lam, Lee and Shimozono, we show that
the leaves in the Edelman-Greene tree of $w$ are in bijection with the
EG-pipedreams of $w$. This allows us to establish a shape preserving one-to-one
correspondence between reduced word tableaux for $w$ and EG-pipedreams of $w$.

0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas