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Physical Sciences and Mathematics Commons™
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Articles 1 - 4 of 4
Full-Text Articles in Physical Sciences and Mathematics
From Dyck Paths To Standard Young Tableaux, Juan B. Gil, Peter R. W. Mcnamara, Jordan O. Tirrell, Michael D. Weiner
From Dyck Paths To Standard Young Tableaux, Juan B. Gil, Peter R. W. Mcnamara, Jordan O. Tirrell, Michael D. Weiner
Faculty Journal Articles
We present nine bijections between classes of Dyck paths and classes of standard Young tableaux (SYT). In particular, we consider SYT of flag and rectangular shapes, we give Dyck path descriptions for certain SYT of height at most 3, and we introduce a special class of labeled Dyck paths of semilength n that is shown to be in bijection with the set of all SYT with n boxes. In addition, we present bijections from certain classes of Motzkin paths to SYT. As a natural framework for some of our bijections, we introduce a class of set partitions which in some …
Orthogonal Groups In Characteristic 2 Acting On Polytopes Of High Rank, Peter A. Brooksbank, Dimitri Leemans, John T. Ferrara
Orthogonal Groups In Characteristic 2 Acting On Polytopes Of High Rank, Peter A. Brooksbank, Dimitri Leemans, John T. Ferrara
Faculty Journal Articles
No abstract provided.
On The Ranks Of String C-Group Representations For Symplectic And Orthogonal Groups, Peter A. Brooksbank
On The Ranks Of String C-Group Representations For Symplectic And Orthogonal Groups, Peter A. Brooksbank
Faculty Journal Articles
We determine the ranks of string C-group representations of 4-dimensional projective symplectic groups over a finite field, and comment on those of higher-dimensional symplectic and orthogonal groups.
Exact Sequences Of Inner Automorphisms Of Tensors, Peter A. Brooksbank
Exact Sequences Of Inner Automorphisms Of Tensors, Peter A. Brooksbank
Faculty Journal Articles
We produce a long exact sequence whose terms are unit groups of associative algebras that behave as inner automorphisms of a given tensor. Our sequence generalizes known sequences for associative and non-associative algebras. In a manner similar to those, our sequence facilitates inductive reasoning about, and calculation of the groups of symmetries of a tensor. The new insights these methods afford can be applied to problems ranging from understanding algebraic structures to distinguishing entangled states in particle physics.