On the sign-imbalance of partition shapes
2005 (English)In: Journal of combinatorial theory. Series A (Print), ISSN 0097-3165, E-ISSN 1096-0899, Vol. 111, no 2, 190-203 p.Article in journal (Refereed) Published
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([n/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 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.
Place, publisher, year, edition, pages
2005. Vol. 111, no 2, 190-203 p.
Chess tableau; Domino; Fourling; Inversion; Robinson-Schensted correspondence; Row insertion; Shape; Sign-balanced; Sign-imbalance; Tableau
IdentifiersURN: urn:nbn:se:kth:diva-6859DOI: 10.1016/j.jcta.2004.12.001ISI: 000231186300002ScopusID: 2-s2.0-22644437823OAI: oai:DiVA.org:kth-6859DiVA: diva2:11688
QC 201008182007-03-092007-03-092010-08-18Bibliographically approved