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AN EXTENSION OF REDUCTION FORMULA FOR LITTLEWOOD-RICHARDSON COEFFICIENTS

  • Cho, Soo-Jin ;
  • Jung, Eun-Kyoung ;
  • Moon, Dong-Ho
  • Received : 2009.02.17
  • Published : 2010.11.01

Abstract

There is a well-known classical reduction formula by Griffiths and Harris for Littlewood-Richardson coefficients, which reduces one part from each partition. In this article, we consider an extension of the reduction formula reducing two parts from each partition. This extension is a special case of the factorization theorem of Littlewood-Richardson coefficients by King, Tollu, and Toumazet (the KTT theorem). This case of the KTT factorization theorem is of particular interest, because, in this case, the KTT theorem is simply a reduction formula reducing two parts from each partition. A bijective proof using tableaux of this reduction formula is given in this paper while the KTT theorem is proved using hives.

Keywords

Littlewood-Richardson coefficients;Reduction formulae

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  2. A BIJECTIVE PROOF OF r = 1 REDUCTION FORMULA FOR LITTLEWOOD-RICHARDSON COEFFICIENTS vol.32, pp.2, 2010, https://doi.org/10.5831/HMJ.2010.32.2.271