English

Checkerboard style Schur multiple zeta values and odd single zeta values

Number Theory 2017-11-28 v2 Combinatorics

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.

Keywords

Cite

@article{arxiv.1711.04746,
  title  = {Checkerboard style Schur multiple zeta values and odd single zeta values},
  author = {Henrik Bachmann and Yoshinori Yamasaki},
  journal= {arXiv preprint arXiv:1711.04746},
  year   = {2017}
}

Comments

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