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Decorated Dyck paths, polyominoes, and the delta conjecture [electronic resource] / Michele D'Adderio, Alessandro Iraci, Anna Vanden Wyngaerd

Author
D'Adderio, Michele
Published
Providence, RI : American Mathematical Society, [2022]
Physical Description
pages cm
Additional Creators
Iraci, Alessandro and Wyngaerd, Anna Vanden
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Contents
Background and definitions -- Conjectures -- Our results -- Symmetric functions -- Combinatorics of decorated Dyck paths -- Combinatorics of polyominoes -- Putting the pieces together -- Square paths.
Summary
"We discuss the combinatorics of decorated Dyck paths and decorated parallelogram polyominoes, extending to the decorated case the main results of both Haglund ("A proof of the Schroder conjecture", 2004) and Aval et al. ("Statistics on parallelogram polyominoes and a analogue of the Narayana numbers", 2014). This settles in particular the cases and of the Delta conjecture of Haglund, Remmel and Wilson ("The delta conjecture", 2018). Along the way, we introduce some new statistics, formulate some new conjectures, prove some new identities of symmetric functions, and answer a few open problems in the literature (e.g., from Aval, Bergeron and Garsia [2015], Haglund, Remmel and Wilson [2018], and Zabrocki [2019]). The main technical tool is a new identity in the theory of Macdonald polynomials that extends a theorem of Haglund in "A proof of the Schroder conjecture" (2004)"--
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ISBN
9781470471576 (paperback)
9781470471705 (pdf)
Note
"July 2022, volume 278, number 1370 (fifth of 6 numbers)."
Bibliography Note
Includes bibliographical references.
View MARC record | catkey: 45638671