Note on a Formula By Todd

Duncan, D. G.

doi:10.1112/jlms/s1-27.2.235

Cited by 6 publications

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“…The w-core and do are independent of the order of removal of the hooks [5], [6]. 3 For a method of evaluating the B ff which does not lead to the recursion formula see [1],…”

Section: Preliminary Definitions and Lemmas Using Thrall's Notation mentioning

confidence: 99%

On D. E. Littlewood's Algebra of S-Functions

Duncan

1952

Can. j. math.

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Several papers have been written on the “new” multiplication of S-functions since Littlewood [3, p. 206] first suggested the problem. M. Zia-ud-Din [13] calculated the case {m} ⊗ {n} for mn ≤ 12, making use of the tables of the characters of the symmetric group of degree mn. Later Thrall [10,pp. 378-382] developed explicit formulae for the cases {m} ⊗ {2},{m} ⊗ {3}, {2} ⊗ {m} (where m is any integer).

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“…The w-core and do are independent of the order of removal of the hooks [5], [6]. 3 For a method of evaluating the B ff which does not lead to the recursion formula see [1],…”

Section: Preliminary Definitions and Lemmas Using Thrall's Notation mentioning

confidence: 99%

On D. E. Littlewood's Algebra of S-Functions

Duncan

1952

Can. j. math.

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“…The following table presents a (non-exhaustive) list of some of the known results in this direction. ]] in terms of Schur functions [18] Since general formulae for the coefficients a ν λ,µ have been elusive, various methods for computing plethysm have been developed [5,6,9,13,14,23,26,35,43,45,46] as well as representation-theoretic approaches [4,11,20,32,33,37].…”

Section: Introductionmentioning

confidence: 99%

The mystery of plethysm coefficients

Colmenarejo¹,

Orellana²,

Saliola³

et al. 2022

Preprint

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Composing two representations of the general linear groups gives rise to Littlewood's (outer) plethysm. On the level of characters, this poses the question of finding the Schur expansion of the plethysm of two Schur functions. A combinatorial interpretation for the Schur expansion coefficients of the plethysm of two Schur functions is, in general, still an open problem. We identify a proof technique of combinatorial representation theory, which we call the "s-perp trick", and point out several examples in the literature where this idea is used. We use the s-perp trick to give algorithms for computing monomial and Schur expansions of symmetric functions. In several special cases, these algorithms are more efficient than those currently implemented in SageMath.

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Combinatorial Algorithms for the Expansion of Various Products of Schur Functions

Remmel

1990

Topics in Computational Algebra

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Note on a Formula By Todd

Cited by 6 publications

References 0 publications

On D. E. Littlewood's Algebra of S-Functions

On D. E. Littlewood's Algebra of S-Functions

The mystery of plethysm coefficients

Combinatorial Algorithms for the Expansion of Various Products of Schur Functions

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