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Journal article
Haglund's conjecture on 3-column Macdonald polynomials
Mathematische Zeitschrift, v 283(1-2), pp 601-628
01 Jun 2016
Abstract
We prove a positive combinatorial formula for the Schur expansion of LLT polynomials indexed by a 3-tuple of skew shapes. This verifies a conjecture of Haglund (Proc Natl Acad Sci USA 101(46):16127-16131, 2004). The proof requires expressing a noncommutative Schur function as a positive sum of monomials in Lam's (Eur J Combin 29(1):343-359, 2008) algebra of ribbon Schur operators. Combining this result with the expression of Haglund et al. (J Am Math Soc 18(3):735-761, 2005) for transformed Macdonald polynomials in terms of LLT polynomials then yields a positive combinatorial rule for transformed Macdonald polynomials indexed by a shape with 3 columns.
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Details
- Title
- Haglund's conjecture on 3-column Macdonald polynomials
- Creators
- Jonah Blasiak - Drexel University
- Publication Details
- Mathematische Zeitschrift, v 283(1-2), pp 601-628
- Publisher
- Springer Nature
- Number of pages
- 28
- Grant note
- DMS-14071174 / NSF; National Science Foundation (NSF)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000374562900027
- Scopus ID
- 2-s2.0-84955257790
- Other Identifier
- 991019168736704721
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- Web of Science research areas
- Mathematics