Matches in SemOpenAlex for { <https://semopenalex.org/work/W2904534706> ?p ?o ?g. }
Showing items 1 to 81 of
81
with 100 items per page.
- W2904534706 endingPage "2899" @default.
- W2904534706 startingPage "2850" @default.
- W2904534706 abstract "Littlewood--Richardson (LR) coefficients $c_{munu}^lambda$ may be evaluated by means of several combinatorial models. These include not only the original one, based on the LR rule for enumerating LR tableaux of skew shape $lambda/mu$ and weight $nu$, but also one based on the enumeration of LR hives with boundary edge labels $lambda$, $mu$, and $nu$. Unfortunately, neither of these reveals in any obvious way the well-known symmetry property $c_{munu}^lambda=c_{numu}^lambda$. Here we introduce a map $sigma^{(n)}$ on LR hives that interchanges contributions to $c_{munu}^lambda$ and $c_{numu}^lambda$ for any partitions $lambda$, $mu$, $nu$ of lengths no greater than $n$, and then we prove that it is a bijection, thereby making manifest the required symmetry property. The map $sigma^{(n)}$ involves repeated path removals from a given LR hive with boundary edge labels $(lambda,mu,nu)$ that give rise to a sequence of hives whose left-hand boundary edge labels define a partner LR hive with boundary edge labels $(lambda,nu,mu)$. A new feature of our hive model is its realization in terms of edge labels and rhombus gradients, with the latter playing a key role in defining the action of path removal operators in a manner designed to preserve the required hive conditions. A consideration of the detailed properties of the path removal procedures also leads to a wholly combinatorial self-contained hive based proof that $sigma^{(n)}$ is an involution." @default.
- W2904534706 created "2018-12-22" @default.
- W2904534706 creator A5003288573 @default.
- W2904534706 creator A5057861201 @default.
- W2904534706 creator A5083842538 @default.
- W2904534706 date "2018-01-01" @default.
- W2904534706 modified "2023-09-25" @default.
- W2904534706 title "The Symmetry of Littlewood--Richardson Coefficients: A New Hive Model Involutory Bijection" @default.
- W2904534706 cites W1664429083 @default.
- W2904534706 cites W1967739927 @default.
- W2904534706 cites W1969379811 @default.
- W2904534706 cites W1975608391 @default.
- W2904534706 cites W1977184999 @default.
- W2904534706 cites W1991467510 @default.
- W2904534706 cites W2009898790 @default.
- W2904534706 cites W2032068668 @default.
- W2904534706 cites W2062660918 @default.
- W2904534706 cites W2087792692 @default.
- W2904534706 doi "https://doi.org/10.1137/17m1162834" @default.
- W2904534706 hasPublicationYear "2018" @default.
- W2904534706 type Work @default.
- W2904534706 sameAs 2904534706 @default.
- W2904534706 citedByCount "4" @default.
- W2904534706 countsByYear W29045347062020 @default.
- W2904534706 countsByYear W29045347062022 @default.
- W2904534706 countsByYear W29045347062023 @default.
- W2904534706 crossrefType "journal-article" @default.
- W2904534706 hasAuthorship W2904534706A5003288573 @default.
- W2904534706 hasAuthorship W2904534706A5057861201 @default.
- W2904534706 hasAuthorship W2904534706A5083842538 @default.
- W2904534706 hasBestOaLocation W29045347062 @default.
- W2904534706 hasConcept C114614502 @default.
- W2904534706 hasConcept C118615104 @default.
- W2904534706 hasConcept C120665830 @default.
- W2904534706 hasConcept C121332964 @default.
- W2904534706 hasConcept C134306372 @default.
- W2904534706 hasConcept C156340839 @default.
- W2904534706 hasConcept C161903591 @default.
- W2904534706 hasConcept C24424167 @default.
- W2904534706 hasConcept C2524010 @default.
- W2904534706 hasConcept C2778113609 @default.
- W2904534706 hasConcept C33923547 @default.
- W2904534706 hasConcept C62354387 @default.
- W2904534706 hasConceptScore W2904534706C114614502 @default.
- W2904534706 hasConceptScore W2904534706C118615104 @default.
- W2904534706 hasConceptScore W2904534706C120665830 @default.
- W2904534706 hasConceptScore W2904534706C121332964 @default.
- W2904534706 hasConceptScore W2904534706C134306372 @default.
- W2904534706 hasConceptScore W2904534706C156340839 @default.
- W2904534706 hasConceptScore W2904534706C161903591 @default.
- W2904534706 hasConceptScore W2904534706C24424167 @default.
- W2904534706 hasConceptScore W2904534706C2524010 @default.
- W2904534706 hasConceptScore W2904534706C2778113609 @default.
- W2904534706 hasConceptScore W2904534706C33923547 @default.
- W2904534706 hasConceptScore W2904534706C62354387 @default.
- W2904534706 hasFunder F4320334764 @default.
- W2904534706 hasFunder F4320334779 @default.
- W2904534706 hasFunder F4320335246 @default.
- W2904534706 hasFunder F4320335322 @default.
- W2904534706 hasIssue "4" @default.
- W2904534706 hasLocation W29045347061 @default.
- W2904534706 hasLocation W29045347062 @default.
- W2904534706 hasOpenAccess W2904534706 @default.
- W2904534706 hasPrimaryLocation W29045347061 @default.
- W2904534706 hasRelatedWork W1496772266 @default.
- W2904534706 hasRelatedWork W2015104084 @default.
- W2904534706 hasRelatedWork W2081350253 @default.
- W2904534706 hasRelatedWork W2112972328 @default.
- W2904534706 hasRelatedWork W2258229947 @default.
- W2904534706 hasRelatedWork W2558105755 @default.
- W2904534706 hasRelatedWork W2569575069 @default.
- W2904534706 hasRelatedWork W2786291196 @default.
- W2904534706 hasRelatedWork W2900158650 @default.
- W2904534706 hasRelatedWork W4319722755 @default.
- W2904534706 hasVolume "32" @default.
- W2904534706 isParatext "false" @default.
- W2904534706 isRetracted "false" @default.
- W2904534706 magId "2904534706" @default.
- W2904534706 workType "article" @default.