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On the sign-imbalance of partition shapes
- Source :
-
Journal of Combinatorial Theory - Series A . Aug2005, Vol. 111 Issue 2, p190-203. 14p. - Publication Year :
- 2005
-
Abstract
- Abstract: 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 . 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 a sharpening of another conjecture by Stanley concerning weighted sums of squares of sign-imbalances. The proof is built on a remarkably simple relation between the sign of a permutation and the signs of its RS-corresponding tableaux. [Copyright &y& Elsevier]
- Subjects :
- *GRAPH theory
*PERMUTATIONS
*ALGEBRA
*COMBINATORICS
Subjects
Details
- Language :
- English
- ISSN :
- 00973165
- Volume :
- 111
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Combinatorial Theory - Series A
- Publication Type :
- Academic Journal
- Accession number :
- 18160018
- Full Text :
- https://doi.org/10.1016/j.jcta.2004.12.001