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Factorisation of Littlewood-Richardson coefficients

Factorisation of Littlewood-Richardson coefficients
Factorisation of Littlewood-Richardson coefficients
The hive model is used to show that the saturation of any essential Horn inequality leads to the factorisation of Littlewood-Richardson coefficients. The proof is based on the use of combinatorial objects known as puzzles. These are shown not only to account for the origin of Horn inequalities, but also to determine the constraints on hives that lead to factorisation. Defining a primitive Littlewood-Richardson coefficient to be one for which all essential Horn inequalities are strict, it is shown that every Littlewood-Richardson coefficient can be expressed as a product of primitive coefficients. Precisely the same result is shown to apply to the polynomials defined by stretched Littlewood-Richardson coefficients.
littlewood-richardson coefficients, hive model, horn inequalities, puzzles, factorisation, lr-polynomials
0097-3165
314-333
King, Ronald C.
76ae9fb3-6b19-449d-8583-dbf1d7ed2706
Tollu, Christophe
3192898d-10d4-46c8-a470-25dd49cb2b9d
Toumazet, Frederic
c371c049-30e5-4538-a184-c35975682fe2
King, Ronald C.
76ae9fb3-6b19-449d-8583-dbf1d7ed2706
Tollu, Christophe
3192898d-10d4-46c8-a470-25dd49cb2b9d
Toumazet, Frederic
c371c049-30e5-4538-a184-c35975682fe2

King, Ronald C., Tollu, Christophe and Toumazet, Frederic (2009) Factorisation of Littlewood-Richardson coefficients. Journal of Combinatorial Theory, Series A, 116 (2), 314-333. (doi:10.1016/j.jcta.2008.06.005).

Record type: Article

Abstract

The hive model is used to show that the saturation of any essential Horn inequality leads to the factorisation of Littlewood-Richardson coefficients. The proof is based on the use of combinatorial objects known as puzzles. These are shown not only to account for the origin of Horn inequalities, but also to determine the constraints on hives that lead to factorisation. Defining a primitive Littlewood-Richardson coefficient to be one for which all essential Horn inequalities are strict, it is shown that every Littlewood-Richardson coefficient can be expressed as a product of primitive coefficients. Precisely the same result is shown to apply to the polynomials defined by stretched Littlewood-Richardson coefficients.

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Published date: February 2009
Keywords: littlewood-richardson coefficients, hive model, horn inequalities, puzzles, factorisation, lr-polynomials

Identifiers

Local EPrints ID: 66211
URI: http://eprints.soton.ac.uk/id/eprint/66211
ISSN: 0097-3165
PURE UUID: 0d2f031d-9544-4595-ab64-befc4495ddd3

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Date deposited: 12 Jan 2010
Last modified: 07 Jan 2022 23:41

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Contributors

Author: Ronald C. King
Author: Christophe Tollu
Author: Frederic Toumazet

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