A BIJECTIVE PROOF OF THE SECOND REDUCTION FORMULA FOR LITTLEWOOD-RICHARDSON COEFFICIENTS

- Journal title : Bulletin of the Korean Mathematical Society
- Volume 45, Issue 3, 2008, pp.485-494
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/BKMS.2008.45.3.485

Title & Authors

A BIJECTIVE PROOF OF THE SECOND REDUCTION FORMULA FOR LITTLEWOOD-RICHARDSON COEFFICIENTS

Cho, Soo-Jin; Jung, Eun-Kyoung; Moon, Dong-Ho;

Cho, Soo-Jin; Jung, Eun-Kyoung; Moon, Dong-Ho;

Abstract

There are two well known reduction formulae for structural constants of the cohomology ring of Grassmannians, i.e., Littlewood-Richardson coefficients. Two reduction formulae are a conjugate pair in the sense that indexing partitions of one formula are conjugate to those of the other formula. A nice bijective proof of the first reduction formula is given in the authors` previous paper while a (combinatorial) proof for the second reduction formula in the paper depends on the identity between Littlewood-Richardson coefficients of conjugate shape. In this article, a direct bijective proof for the second reduction formula for Littlewood-Richardson coefficients is given. Our proof is independent of any previously known results (or bijections) on tableaux theory and supplements the arguments on bijective proofs of reduction formulae in the authors` previous paper.

Keywords

reduction formulae;Littlewood-Richardson coefficient;Schubert calculus;

Language

English

Cited by

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A BIJECTIVE PROOF OF r = 1 REDUCTION FORMULA FOR LITTLEWOOD-RICHARDSON COEFFICIENTS,;

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