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Decorated Dyck paths, polyominoes, and the delta conjecture
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 N...
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| Auteurs principaux : | , , |
|---|---|
| Format : | Livre |
| Langue : | anglais |
| Titre complet : | Decorated Dyck paths, polyominoes, and the delta conjecture / Michele D'Adderio, Alessandro Iraci, Anna Vanden Wyngaerd |
| Publié : |
Providence (R.I.) :
American Mathematical Society
, 2022 |
| Description matérielle : | 1 vol. (XI-119 p.) |
| Collection : | Memoirs of the American Mathematical Society ; 1370 |
| Sujets : |
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| 200 | 1 | |a Decorated Dyck paths, polyominoes, and the delta conjecture |f Michele D'Adderio, Alessandro Iraci, Anna Vanden Wyngaerd | |
| 214 | 0 | |a Providence (R.I.) |c American Mathematical Society |d 2022 | |
| 215 | |a 1 vol. (XI-119 p.) |c fig. |d 26 cm | ||
| 225 | 2 | |a Memoirs of the American Mathematical Society |x 0065-9266 |v number 1370 | |
| 300 | |a "July 2022, volume 278, number 1370 (fifth of 6 numbers)." | ||
| 320 | |a Bibliogr. p. 117-119 | ||
| 330 | |a 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) |2 résumé des auteurs | ||
| 359 | 2 | |b Background and definitions |b Conjectures |b Our results |b Symmetric functions |b Combinatorics of decorated Dyck paths |b Combinatorics of polyominoes |b Putting the pieces together |b Square paths | |
| 410 | | | |0 013293931 |t Memoirs of the American Mathematical Society |x 0065-9266 |v 1370 | |
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| 701 | 1 | |3 PPN264813537 |a Vanden Wyngaerd |b Anna |f 19..-.... |4 070 | |
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