Matches in SemOpenAlex for { <https://semopenalex.org/work/W2143292021> ?p ?o ?g. }
Showing items 1 to 96 of
96
with 100 items per page.
- W2143292021 abstract "Garsia and Haiman (J. Algebraic. Combin. $bf5$ $(1996)$, $191-244$) conjectured that a certain sum $C_n(q,t)$ of rational functions in $q,t$ reduces to a polynomial in $q,t$ with nonnegative integral coefficients. Haglund later discovered (Adv. Math., in press), and with Garsia proved (Proc. Nat. Acad. Sci. ${bf98}$ $(2001)$, $4313-4316$) the refined conjecture $C_n(q,t) = sum q^{{rm area}}t^{{rm bounce}}$. Here the sum is over all Catalan lattice paths and ${rm area}$ and ${rm bounce}$ have simple descriptions in terms of the path. In this article we give an extension of $({rm area},{rm bounce})$ to Schröder lattice paths, and introduce polynomials defined by summing $q^{{rm area}}t^{{rm bounce}}$ over certain sets of Schröder paths. We derive recurrences and special values for these polynomials, and conjecture they are symmetric in $q,t$. We also describe a much stronger conjecture involving rational functions in $q,t$ and the $nabla$ operator from the theory of Macdonald symmetric functions." @default.
- W2143292021 created "2016-06-24" @default.
- W2143292021 creator A5001425355 @default.
- W2143292021 creator A5078112701 @default.
- W2143292021 creator A5080635755 @default.
- W2143292021 creator A5088061652 @default.
- W2143292021 date "2003-04-23" @default.
- W2143292021 modified "2023-10-17" @default.
- W2143292021 title "A Schröder Generalization of Haglund's Statistic on Catalan Paths" @default.
- W2143292021 cites W1634042400 @default.
- W2143292021 cites W1671066123 @default.
- W2143292021 cites W2008052995 @default.
- W2143292021 cites W2022892305 @default.
- W2143292021 cites W2042843318 @default.
- W2143292021 cites W2046479912 @default.
- W2143292021 cites W2059036144 @default.
- W2143292021 cites W2087941871 @default.
- W2143292021 cites W2134984950 @default.
- W2143292021 cites W2140141642 @default.
- W2143292021 cites W2327812169 @default.
- W2143292021 cites W2914659449 @default.
- W2143292021 doi "https://doi.org/10.37236/1709" @default.
- W2143292021 hasPublicationYear "2003" @default.
- W2143292021 type Work @default.
- W2143292021 sameAs 2143292021 @default.
- W2143292021 citedByCount "27" @default.
- W2143292021 countsByYear W21432920212012 @default.
- W2143292021 countsByYear W21432920212013 @default.
- W2143292021 countsByYear W21432920212014 @default.
- W2143292021 countsByYear W21432920212015 @default.
- W2143292021 countsByYear W21432920212016 @default.
- W2143292021 countsByYear W21432920212017 @default.
- W2143292021 countsByYear W21432920212018 @default.
- W2143292021 countsByYear W21432920212019 @default.
- W2143292021 countsByYear W21432920212020 @default.
- W2143292021 countsByYear W21432920212022 @default.
- W2143292021 crossrefType "journal-article" @default.
- W2143292021 hasAuthorship W2143292021A5001425355 @default.
- W2143292021 hasAuthorship W2143292021A5078112701 @default.
- W2143292021 hasAuthorship W2143292021A5080635755 @default.
- W2143292021 hasAuthorship W2143292021A5088061652 @default.
- W2143292021 hasBestOaLocation W21432920211 @default.
- W2143292021 hasConcept C101044782 @default.
- W2143292021 hasConcept C114614502 @default.
- W2143292021 hasConcept C118615104 @default.
- W2143292021 hasConcept C121332964 @default.
- W2143292021 hasConcept C134306372 @default.
- W2143292021 hasConcept C177148314 @default.
- W2143292021 hasConcept C202444582 @default.
- W2143292021 hasConcept C24890656 @default.
- W2143292021 hasConcept C2780990831 @default.
- W2143292021 hasConcept C2781204021 @default.
- W2143292021 hasConcept C33923547 @default.
- W2143292021 hasConcept C3746008 @default.
- W2143292021 hasConcept C43929256 @default.
- W2143292021 hasConcept C52153879 @default.
- W2143292021 hasConcept C75190567 @default.
- W2143292021 hasConcept C90119067 @default.
- W2143292021 hasConcept C9376300 @default.
- W2143292021 hasConceptScore W2143292021C101044782 @default.
- W2143292021 hasConceptScore W2143292021C114614502 @default.
- W2143292021 hasConceptScore W2143292021C118615104 @default.
- W2143292021 hasConceptScore W2143292021C121332964 @default.
- W2143292021 hasConceptScore W2143292021C134306372 @default.
- W2143292021 hasConceptScore W2143292021C177148314 @default.
- W2143292021 hasConceptScore W2143292021C202444582 @default.
- W2143292021 hasConceptScore W2143292021C24890656 @default.
- W2143292021 hasConceptScore W2143292021C2780990831 @default.
- W2143292021 hasConceptScore W2143292021C2781204021 @default.
- W2143292021 hasConceptScore W2143292021C33923547 @default.
- W2143292021 hasConceptScore W2143292021C3746008 @default.
- W2143292021 hasConceptScore W2143292021C43929256 @default.
- W2143292021 hasConceptScore W2143292021C52153879 @default.
- W2143292021 hasConceptScore W2143292021C75190567 @default.
- W2143292021 hasConceptScore W2143292021C90119067 @default.
- W2143292021 hasConceptScore W2143292021C9376300 @default.
- W2143292021 hasIssue "1" @default.
- W2143292021 hasLocation W21432920211 @default.
- W2143292021 hasLocation W21432920212 @default.
- W2143292021 hasOpenAccess W2143292021 @default.
- W2143292021 hasPrimaryLocation W21432920211 @default.
- W2143292021 hasRelatedWork W1509938291 @default.
- W2143292021 hasRelatedWork W1511502611 @default.
- W2143292021 hasRelatedWork W1881371619 @default.
- W2143292021 hasRelatedWork W2143292021 @default.
- W2143292021 hasRelatedWork W2238316922 @default.
- W2143292021 hasRelatedWork W2307800030 @default.
- W2143292021 hasRelatedWork W2334364575 @default.
- W2143292021 hasRelatedWork W2617099550 @default.
- W2143292021 hasRelatedWork W2921483360 @default.
- W2143292021 hasRelatedWork W3008734763 @default.
- W2143292021 hasVolume "10" @default.
- W2143292021 isParatext "false" @default.
- W2143292021 isRetracted "false" @default.
- W2143292021 magId "2143292021" @default.
- W2143292021 workType "article" @default.