2015/10/23 by Amitai Regev, Doron Zeilberger, Regev, Amitai +1
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · Mathematics · #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Finite Group Theory Research #Genomics and Chromatin Dynamics #Topological and Geometric Data Analysis #graph theory and CDMA systems #math.CO
paper · pdf · doi:10.48550/arxiv.1510.07061
5 pages
arxiv created 2015/10/23 · openalex publication_date 2015/10/23 · arxiv updated 2015/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In a recent article (arXiv:1507.03499) (joint with Alon Regev) we studied sums of squares of characters Chi(L,M) of the Symmetric Group over shapes L that are two-rowed, and shapes L that are hook shapes, and M is an arbitrary shape that mostly consists of ones, and designed algorithms for closed-form evaluations of each of these. We noted (and proved) that when M is the shape with n cells consisting of 3 followed by n-3 ones, the former sum equals one half time the analogous sum over hook shapes with n+2 cells and M is the partition consisting of 3,2, followed by n-3 ones. Here we show that this is just a tip of an iceberg, and prove (alas, by purely human means) that the former sum with M consisting of all odd parts, and (possibly) a consecutive string of powers of 2, starting at 2, equals one half of the latter sum where M is replaced by a partition where all the odd parts are retained but the consecutive string of powers of 2: 2,4, ..., 2t-1 is replaced by 2t.