Enumerative combinatorics
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
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The Robinson-Schensted correspondence maps a permutation onto a pair of standard Young tableaux of the same shape. The shape of the two tableaux is referred to as the shape of the permutation. By using the theory of Kazhdan-Luszitg, Hohlweg has recently characterized the permutations with a fixed shape and a minimal inversion number. The present note provides a combinatorial proof of this result by using Viennot's geometric algorithm of the Robinson-Schensted correspondence.