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pro vyhledávání: '"Donley Jr., Robert W."'
We survey the combinatorics of the Adinkra, a graphical device for solving differential equations in supersymmetry. These graphs represent an exceptional class of 1-factorizations with further augmentations. As a new feature, we characterize Adinkras
Externí odkaz:
http://arxiv.org/abs/2410.12834
The finite Young lattice $L(m, n)$ is rank-symmetric, rank-unimodal, and has the strong Sperner property. R. Stanley further conjectured that $L(m, n)$ admits a symmetric chain order. We show that the order structure on $L(m, n)$ is equivalent to a n
Externí odkaz:
http://arxiv.org/abs/2407.20008
Autor:
Donley, Jr., Robert W., Kim, Won Geun
Similar to how standard Young tableaux represent paths in the Young lattice, Latin rectangles may be use to enumerate paths in the poset of semi-magic squares with entries zero or one. The symmetries associated to determinant preserve this poset, and
Externí odkaz:
http://arxiv.org/abs/2202.06318
Autor:
Donley Jr, Robert W.
After reviewing the group structure and representation theory for the dihedral group $D_{2n},$ we consider an intertwining operator $\Phi_\rho$ from the group algebra $\mathbb{C}[D_{2n}]$ into a corresponding space of semi-magic matrices. From this i
Externí odkaz:
http://arxiv.org/abs/2110.14487
Autor:
Donley Jr, Robert W.
We give formulas for enumerating directed paths in the graded poset of semi-magic squares of size three. We give two applications of these formulas: an advanced example of Vandermonde convolution for finite graded posets, and a direct method for deri
Externí odkaz:
http://arxiv.org/abs/2107.09463
Autor:
Donley, Jr, Robert W.
In previous work on Clebsch-Gordan coefficients, certain remarkable hexagonal arrays of integers are constructed that display behaviors found in Pascal's Triangle. We explain these behaviors further using the binomial transform and discrete convoluti
Externí odkaz:
http://arxiv.org/abs/1905.01525
Autor:
Donley Jr, Robert W.
Publikováno v:
Combinatorial and additive number theory III. Springer Proc. in Math. and Stat. 297, 75-100, Springer, NY (2019)
We develop further properties of the matrices $M(m, n, k)$ defined by the author and W. G. Kim in a previous work. In particular, we continue an alternative approach to the theory of Clebsch-Gordan coefficients in terms of combinatorics and convex ge
Externí odkaz:
http://arxiv.org/abs/1810.00616
Autor:
Donley Jr., Robert W., Kim, Won Geun
Publikováno v:
Representation theory and harmonic analysis on symmetric spaces. Contemp. Math. 714, 115-130, AMS, Providence (2018)
A theory of Clebsch-Gordan coefficients for $SL(2, C)$ is given using only rational numbers. Features include orthogonality relations, recurrence relations, and Regge's symmetry group. Results follow from elementary representation theory and properti
Externí odkaz:
http://arxiv.org/abs/1707.03022