Permutation Sign under the Robinson-Schensted Correspondence
نویسنده
چکیده
We show how the sign of a permutation can be deduced from the tableaux induced by the permutation under the Robinson-Schensted correspondence. The result yields a simple proof of a conjecture on the squares of imbalances raised recently by Stanley.
منابع مشابه
Permutation Sign under the Robinson-schensted-knuth Correspondence
We show how the sign of a permutation can be deduced from the tableaux induced by the permutation under the Robinson-Schensted-Knuth correspondence. The result yields a simple proof of a conjecture on the squares of imbalances raised by Stanley.
متن کاملOn the sign-imbalance of partition shapes
Let the sign of a standard Young tableau be the sign of the permutation you get by reading it row by row from left to right, like a book. A conjecture by Richard Stanley says that the sum of the signs of all SYTs with n squares is 2. We present a stronger theorem with a purely combinatorial proof using the Robinson-Schensted correspondence and a new concept called chess tableaux. We also prove ...
متن کاملOn the sign-imbalance of skew partition shapes
Let the sign of a skew standard Young tableau be the sign of the permutation you get by reading it row by row from left to right, like a book. We examine how the sign property is transferred by the skew Robinson-Schensted correspondence invented by Sagan and Stanley. The result is a remarkably simple generalization of the ordinary non-skew formula. The sum of the signs of all standard tableaux ...
متن کاملProperties of the nonsymmetric Robinson-Schensted-Knuth algorithm
We introduce a generalization of the Robinson-Schensted-Knuth algorithm to composition tableaux involving an arbitrary permutation. If the permutation is the identity our construction reduces to Mason’s original composition Robinson-Schensted-Knuth algorithm. In particular we develop an analogue of Schensted insertion in our more general setting, and use this to obtain new decompositions of the...
متن کاملRefined sign-balance on 321-avoiding permutations
The number of even 321-avoiding permutations of length n is equal to the number of odd ones if n is even, and exceeds it by the n−1 2 th Catalan number otherwise. We present an involution that proves a refinement of this sign-balance property respecting the length of the longest increasing subsequence of the permutation. In addition, this yields a combinatorial proof of a recent analogous resul...
متن کامل