Principal specializations of Schubert polynomials and pattern containment
Abstract
We show that the principal specialization of the Schubert polynomial at w is bounded below by 1+p132(w)+p1432(w) where pu(w) is the number of occurrences of the pattern u in w, strengthening a previous result by A. Weigandt. We then make a conjecture relating the principal specialization of Schubert polynomials to pattern containment. Finally, we characterize permutations w whose RC-graphs are connected by simple ladder moves via pattern avoidance.
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