Tableau atoms and a new Macdonald positivity conjecture Duke Math J

By Luc Lapointe, Alain Lascoux, Jennifer Morse. 2000

108 citations recorded by the source corpus.

A snap action fluid control valve, the operation of which is controlled by a relatively slow acting thermally responsive actuator member. The valve of this invention is particularly adapted for use in controlling flow of fluid to a fluid operable clutch or the like for operation thereof. The thermally responsive actuator portion of the valve senses temperature of a fluid, the temperature of which is responsive to operation of a fan which is operated through the clutch.

Subfields: Algebra and Number Theory, Applied Mathematics, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/73e8e8e701ec9dcb015b5ae8b079413ee977ceb9

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In Algebra and Number Theory

In Applied Mathematics

In Discrete Mathematics and Combinatorics

Citations in the corpus

Schubert polynomials for the affine Grassmannian (2006, methodology): “These results were conjectures of Mark Shimozono (in the cohomology case, the conjecture was made precise by Jennifer Morse).”
K-theory Schubert calculus of the affine Grassmannian (2009, background): “unctions {s(k) v (x) |v∈WI af}[LLM, LM07] are the basis of Λ(n) dual to {Fv(x) |v∈WI af}, and are usually labeled by the k-bounded partitions {λ|λ1 <n}. (The k-Schur functions originally deﬁned in [LLM] depend on an additional parameter t, and setting t= 1 conjecturally gives the k-Schur function”
A k-tableau characterization of k-Schur functions (2005, background): “This involution acts simply on a Schur function by ωsλ = sλ′ , (4) where λ′ is the partition conjugate to λ. Recent developments in symmetric function theory involved the study of Macdonald polynomials.”
Affine Stanley symmetric functions (2005, background): “I thank Jennifer Morse for interesting discussions about k-Schur functions and dual k-Schur functions.”
k-Schur Functions and Affine Schubert Calculus (2013, methodology): “Lapointe, Lascoux, and Morse [92] conjectured that the Macdonald symmetric functions expand positively in terms of k-Schur functions.”
Affine Insertion and Pieri Rules for the Affine Grassmannian (2006, methodology): “ 11∗ 2 1 1∗ 1∗ 12 1∗ 1 1∗ 2 11 12 11 1∗ 1 1 ∗ 2 11.3. Monomial expansion of t-dependent k-Schur functions. Theorem 11.5 allows us to give a conjectural monomial expansion for the k-Schur functions of [14, 15] which depend on a parameter t. Suppose C= µ−→i,j λ is a marked strong cover of k+ 1-cores. ”
Tableaux on k+1-cores, reduced words for affine permutations, and k-Schur expansions (2004, methodology): “4) we accordingly, in our previous work [9], defined μ →k λ in terms of the involution μ 7→ μk by μ →k λ ⇐⇒ |λ| = |μ|+ 1 & μ ⊆ λ & μ ωk ⊆ λk .”