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http://dx.doi.org/10.4134/BKMS.2008.45.3.485

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

Cho, Soo-Jin (DEPARTMENT OF MATHEMATICS AJOU UNIVERSITY)
Jung, Eun-Kyoung (DEPARTMENT OF MATHEMATICS AJOU UNIVERSITY)
Moon, Dong-Ho (DEPARTMENT OF APPLIED MATHEMATICS SEJONG UNIVERSITY)
Publication Information
Bulletin of the Korean Mathematical Society / v.45, no.3, 2008 , pp. 485-494 More about this Journal
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;
Citations & Related Records

Times Cited By Web Of Science : 3  (Related Records In Web of Science)
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