Checkerboard style Schur multiple zeta values and odd single zeta values

2017/11/13 by Henrik Bachmann, Bachmann, Henrik, Yoshinori Yamasaki +1 · 1 citation
Mathematics · #05E05 #11M41 #33C05 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #math.CO #math.NT #msc:05E05 #msc:11M41 #msc:33C05

paper · pdf · doi:10.48550/arxiv.1711.04746

21 pages. Added Corollary 3.7 and the case (a,b)=(1,2) in Section 5

arxiv created 2017/11/25 · arxiv updated 2017/11/28

Abstract

We give explicit formulas for the recently introduced Schur multiple zeta values, which generalize multiple zeta(-star) values and which assign to a Young tableaux a real number. In this note we consider Young tableaux of various shapes, filled with alternating entries like a Checkerboard. In particular we obtain new sum representation for odd single zeta values in terms of these Schur multiple zeta values. As a special case we show that some Schur multiple zeta values of Checkerboard style, filled with 1 and 3, are given by determinants of matrices with odd single zeta values as entries.

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