Séminaire Lotharingien de Combinatoire, B74a (2015), 11 pp.
Colleen Ross and Alexander Yong
Combinatorial Rules for Three Bases of Polynomials
We present combinatorial rules (one theorem and two conjectures)
concerning three bases of
First, we prove a "splitting" rule for the basis of Key polynomials
[Demazure, Bull. Sci. Math. 98 (1974), 163-172],
thereby establishing a new positivity theorem about them.
Second, we introduce an extension of Kohnert's
[Bayreuth. Math. Schriften 38 (1990), 1-97]
"moves" to conjecture
the first combinatorial rule for a certain deformation
[Lascoux, in: Physics and Combinatorics,
World Scientific Publishing, 2001, pp. 164-179]
the Key polynomials. Third, we use the same extension to
conjecture a new rule for the Grothendieck polynomials
[Lascoux and Schützenberger, C. R. Acad. Sci. Paris
Sér. I Math.
295 (1982), 629-633].
Received: November 6, 2013.
Revised: April 10, 2015.
Accepted: July 21, 2015.
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