Results 51 to 60 of about 104 (103)
Forum of Mathematics, SigmaWe construct a novel family of difference-permutation operators and prove that they are diagonalized by the wreath Macdonald P-polynomials; the eigenvalues are written in terms of elementary symmetric polynomials of arbitrary degree.
Daniel Orr, Mark Shimozono, Joshua Wen
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DUAL EQUIVALENCE GRAPHS I: A NEW PARADIGM FOR SCHUR POSITIVITY
Forum of Mathematics, Sigma, 2015 We make a systematic study of a new combinatorial construction called a dual equivalence graph. We axiomatize these graphs and prove that their generating functions are symmetric and Schur positive.
SAMI H. ASSAF
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Growth diagram proofs for the Littlewood identities [PDF]
The (dual) Cauchy identity has an easy algebraic proof utilising a commutation relation between the up and (dual) down operators. By using Fomin's growth diagrams, a bijective proof of the commutation relation can be "bijectivised" to obtain RSK like ...
Schreier-Aigner, Florian
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Measures and generalizations of dual Littlewood identities
Forum of Mathematics, SigmaWe introduce three families of vectors |λ―so⟩ $|\underline {\lambda }^{so}\rangle $ vertical bar lamda underbar Superscript s o Baseline right angle bracket , |λ―sp⟩ $|\underline {\lambda }^{sp}\rangle $ vertical bar lamda underbar Superscript s
Zhongren Cai +4 more
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Marked bumpless pipedreams and compatible pairs
We construct a bijection between marked bumpless pipedreams with reverse compatible pairs, which are in bijection with not-necessarily-reduced pipedreams. This directly unifies various formulas for Grothendieck polynomials in the literature.
Mark Shimozono, Tianyi Yu, Daoji Huang
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Combinatorial formulas for shifted dual stable Grothendieck polynomials
Forum of Mathematics, SigmaThe K-theoretic Schur P- and Q-functions $G\hspace {-0.2mm}P_\lambda $ and $G\hspace {-0.2mm}Q_\lambda $ may be concretely defined as weight-generating functions for semistandard shifted set-valued tableaux.
Joel Lewis, Eric Marberg
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YANG–BAXTER FIELD FOR SPIN HALL–LITTLEWOOD SYMMETRIC FUNCTIONS
Forum of Mathematics, Sigma, 2019 Employing bijectivization of summation identities, we introduce local stochastic moves based on the Yang–Baxter equation for $U_{q}(\widehat{\mathfrak{sl}_{2}})$.
ALEXEY BUFETOV, LEONID PETROV
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Discussiones Mathematicae - General Algebra and Applications, 2020 In this paper, we define and study the bivariate complex Fibonacci and Lucas polynomials. We introduce a operator in order to derive some new symmetric properties of bivariate complex Fibonacci and bivariate complex Lucas polynomials, and give the ...
Boughaba Souhila +2 more
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STABILITY PATTERNS IN REPRESENTATION THEORY
Forum of Mathematics, Sigma, 2015 We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories.
STEVEN V SAM, ANDREW SNOWDEN
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Splines on Cayley graphs of the symmetric group
Forum of Mathematics, SigmaA spline is an assignment of polynomials to the vertices of a graph whose edges are labeled by ideals, where the difference of two polynomials labeling adjacent vertices must belong to the corresponding ideal. The set of splines forms a ring. We consider
Nathan R. T. Lesnevich
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