Factorizations of Symmetric Macdonald Polynomials [PDF]
Symmetry, 2018 We prove many factorization formulas for highest weight Macdonald polynomials indexed by particular partitions called quasistaircases. Consequently, we prove a conjecture of Bernevig and Haldane stated in the context of the fractional quantum Hall effect theory.
Laura Colmenarejo +2 more
openalex +8 more sources
Strong factorization property of Macdonald polynomials and higher-order Macdonald's positivity conjecture [PDF]
J. Algebraic Combin., 46 (1), 135-163, 2017, 2016 We prove a strong factorization property of interpolation Macdonald polynomials when $q$ tends to $1$. As a consequence, we show that Macdonald polynomials have a strong factorization property when $q$ tends to $1$, which was posed as an open question in our previous paper with F\'eray. Furthermore, we introduce multivariate $q,t$-Kostka numbers and we
Maciej Dołęga
arxiv +3 more sources
A bijective proof of a factorization formula for Macdonald polynomials at roots of unity [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 We give a combinatorial proof of the factorization formula of modified Macdonald polynomials $\widetilde{H}_{\lambda} (X;q,t)$ when $t$ is specialized at a primitive root of unity.
F. Descouens, H. Morita, Y. Numata
doaj +3 more sources
Prediction of body condition score throughout lactation by random regression test-day models. [PDF]
J Anim Breed GenetAbstract Regular monitoring of body condition score (BCS) changes during lactation is a crucial management tool in dairy cattle; however, the current BCS measurements are often discontinuous and unevenly spaced in time. The aim of this study was to investigate the ability of random regression test‐day models (RR‐TDM) to predict BCS for the entire ...
Atashi H +4 more
europepmc +2 more sources
Macdonald polynomials for super-partitions [PDF]
Physics Letters BWe introduce generalization of famous Macdonald polynomials for the case of super-Young diagrams that contain half-boxes on the equal footing with full boxes. These super-Macdonald polynomials are polynomials of extended set of variables: usual $p_k$ variables are accompanied by anti-commuting Grassmann variables $\theta_k$.
Dmitry Galakhov +2 more
arxiv +3 more sources
Vector valued Macdonald polynomials [PDF]
arXiv, 2011 This paper defines and investigates nonsymmetric Macdonald polynomials with values in an irreducible module of the Hecke algebra of type $A_{N-1}$. These polynomials appear as simultaneous eigenfunctions of Cherednik operators. Several objects and properties are analyzed, such as the canonical bilinear form which pairs polynomials with those arising ...
Dunkl, Charles F., Luque, Jean-Gabriel
arxiv +5 more sources
Highest weight Macdonald and Jack polynomials [PDF]
Journal of Physics A: Mathematical and Theoretical, 2011 17 pages, published ...
Thierry Jolicœur, Jean-Gabriel Luque
+8 more sources
A positivity result in the theory of Macdonald polynomials. [PDF]
Proc Natl Acad Sci U S A, 2001 Garsia AM, Haglund J.
europepmc +3 more sources
Theta Functions, Elliptic Hypergeometric Series, and Kawanaka's Macdonald Polynomial Conjecture [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2009 We give a new theta-function identity, a special case of which is utilised to prove Kawanaka's Macdonald polynomial conjecture. The theta-function identity further yields a transformation formula for multivariable elliptic hypergeometric series which ...
Robin Langer +2 more
doaj +2 more sources
Combinatorial theory of Macdonald polynomials I: proof of Haglund's formula. [PDF]
Proc Natl Acad Sci U S A, 2005 Haglund J, Haiman M, Loehr N.
europepmc +2 more sources