DSpace Collection:
http://hdl.handle.net/10316/15544
2020-07-01T19:50:14ZMultiplicity-free skew Schur functions with full interval support
http://hdl.handle.net/10316/89667
Title: Multiplicity-free skew Schur functions with full interval support
Authors: Azenhas, Olga; Conflitti, Alessandro; Mamede, Ricardo
Abstract: It is known that the Schur expansion of a skew Schur function runs over the interval of partitions, equipped with dominance order, defined by the least and the most dominant Littlewood-Richardson filling of the skew shape. We characterise skew Schur functions (and therefore the product of two Schur functions) which are multiplicity-free and the resulting Schur expansion runs over the whole interval of partitions, i.e., skew Schur functions having Littlewood-Richardson coefficients always equal to 1 over the full interval.2019-01-01T00:00:00ZThe symmetry of Littlewood-Richardson coefficients: a new hive model involutory bijection
http://hdl.handle.net/10316/89666
Title: The symmetry of Littlewood-Richardson coefficients: a new hive model involutory bijection
Authors: Terada, Itaru; King, Ronald C; Azenhas, Olga
Abstract: Littlewood--Richardson (LR) coefficients c^{\lambda}_{\mu\nu} 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^{\lambda}_{\mu\nu} = c^{\lambda}_{\nu\mu}. Here we introduce a map \sigma^(n) on LR hives that interchanges contributions to c^{\lambda}_{\mu\nu} and c^{\lambda}_{\nu\mu} 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 selfcontained hive based proof that \sigma^(n) is an involution.2018-01-01T00:00:00ZDecompositions of linear spaces induced by n-linear maps
http://hdl.handle.net/10316/89499
Title: Decompositions of linear spaces induced by n-linear maps
Authors: Calderón, Antonio Jesús; Kaygorodov, Ivan; Saraiva, Paulo
Abstract: Let V be an arbitrary linear space and f : V x ... x V \rightarrow V an n-linear map. It is proved that, for each choice of a basis B of V, the n-linear map f induces a (nontrivial) decomposition V = \oplus V_j as a direct sum of linear subspaces of V, with respect to B. It is shown that this decomposition is f-orthogonal in the sense that f(V, ..., V_j, ..., V_k,..., V) = 0 when j \neq k, and in such a way that any V_j is strongly f-invariant, meaning that f(V, ..., V_j, ..., V) \subset V_j. A sufficient condition for two different decompositions of V induced by an n-linear map f, with respect to two different bases of V, being isomorphic is deduced. The f-simplicity - an analogue of the usual
simplicity in the framework of n-linear maps - of any linear subspace V_j of a certain decomposition induced by f is characterized. Finally, an application to the structure theory of arbitrary n-ary algebras is provided. This work is a close generalization the results obtained by Calderón (2018).2019-01-01T00:00:00ZFinitely Presentable Algebras For Finitary Monads
http://hdl.handle.net/10316/89490
Title: Finitely Presentable Algebras For Finitary Monads
Authors: Adámek, Jiří; Milius, Stefan; Sousa, Lurdes; Wissmann, Thorsten
Abstract: For finitary regular monads T on locally finitely presentable categories we characterize the finitely presentable objects in the category of T-algebras in the style known from general algebra: they are precisely the algebras presentable by finitely many generators and finitely many relations.2019-01-01T00:00:00Z