The Symmetric Group

By T. Inui, Y. Tanabe, Y. Onodera. 1990

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Citations in the corpus

Covariant Compositional Networks For Learning Graphs (2018, background): “The representation theory of symmetric groups is a rich subject that goes beyond the scope of the present paper (Sagan, 2001).”
On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groups (2018, background): “Unfortunately, the representation theory of symmetric groups is beyond the scope of the present paper (Sagan, 2001).”
Random walks on trees and matchings (2002, background): “For characters of the symmetric group see Sagan (2001) or (Macdonald, 1995, Chapter 1).”
Representations of the Infinite Symmetric Group (2016, methodology): “justified collection of n boxes containing λi boxes in the ith row, counting from top to bottom (Sagan [107, Definition 2.1.1]).”
Advanced Determinant Calculus: A Complement (2005, background): “” For all undefined notation, I refer the reader to standard texts on the representation theory of symmetric groups, as for example [82, 83, 146].”
Skew quasisymmetric Schur functions and noncommutative Schur functions (2010, methodology): “The elementary moves described above that define dual Knuth relations between permutations are of two types [53].”
Kazhdan–Lusztig immanants and products of matrix minors (2006, background): “(See [27, 30] for information on Jacobi-Trudi matrices, and [13] for connections to total nonnegativity.”
Walks with small steps in the quarter plane (2008, methodology): “These walks are thus in bijection with Young tableaux of height at most 3 (Figure 3), or, via the Schensted correspondence [49], with involutions having no decreasing subsequence of length 4.”
Möbius functions and semigroup representation theory II: Character formulas and multiplicities (2006, background): “If μ is a partition of r, let χ denote the irreducible character of Sr associated to μ [37].”