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Full-Text Articles in Algebra
Quasisymmetric Functions Distinguishing Trees, Jean-Christophe Aval, Karimatou Djenabou, Peter R. W. Mcnamara
Quasisymmetric Functions Distinguishing Trees, Jean-Christophe Aval, Karimatou Djenabou, Peter R. W. Mcnamara
Faculty Journal Articles
A famous conjecture of Stanley states that his chromatic symmetric function distinguishes trees. As a quasisymmetric analogue, we conjecture that the chromatic quasisymmetric function of Shareshian and Wachs and of Ellzey distinguishes directed trees. This latter conjecture would be implied by an affirmative answer to a question of Hasebe and Tsujie about the P-partition enumerator distinguishing posets whose Hasse diagrams are trees. They proved the case of rooted trees and our results include a generalization of their result.
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 the groups PSp(4,q)=Ω(5,q), and comment on those of higher-dimensional symplectic and orthogonal groups.
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.
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.
Rank Reduction Of String C-Group Representations, Peter A. Brooksbank, Dimitri Leemans
Rank Reduction Of String C-Group Representations, Peter A. Brooksbank, Dimitri Leemans
Faculty Journal Articles
We show that a rank reduction technique for string C-group representations first used in [Adv. Math. 228 (2018), pp. 3207–3222] for the symmetric groups generalizes to arbitrary settings. The technique permits us, among other things, to prove that orthogonal groups defined on d-dimensional modules over fields of even order greater than 2 possess string C-group representations of all ranks. The broad applicability of the rank reduction technique provides fresh impetus to construct, for suitable families of groups, string C-groups of highest possible rank. It also suggests that the alternating group Alt(11)—the only known group having “rank gaps”—is perhaps more unusual …
Polytopes Of Large Rank For Psl(4,Q), Peter A. Brooksbank, Dimitri Leemans
Polytopes Of Large Rank For Psl(4,Q), Peter A. Brooksbank, Dimitri Leemans
Faculty Journal Articles
This paper examines abstract regular polytopes whose automorphism group is the projective special linear group PSL(4,q). For q odd we show that polytopes of rank 4 exist by explicitly constructing PSL(4,q) as a string C-group of that rank. On the other hand, we show that no abstract regular polytope exists whose group of automorphisms is PSL(4,2k).