Journal of Integer Sequences, Vol. 14 (2011), Article 11.2.4

Combinatorial Remarks on the Cyclic Sum Formula for Multiple Zeta Values

Shingo Saito and Tatsushi Tanaka
Faculty of Mathematics
Kyushu University
744, Motooka, Nishi-ku
Fukuoka, 819-0395

Noriko Wakabayashi
Faculty of Engineering
Kyushu Sangyo University
3-1, Matsukadai 2-chome, Higashi-ku
Fukuoka, 813-8503


The multiple zeta values are generalizations of the values of the Riemann zeta function at positive integers. They are known to satisfy a number of relations, among which are the cyclic sum formula. The cyclic sum formula can be stratified via linear operators defined by the second and third authors. We give the number of relations belonging to each stratum by combinatorial arguments.

Full version:  pdf,    dvi,    ps,    latex    

(Concerned with sequences A000012 A000032 A000079 A000204 A000931 A001644 A001648 A023424 A038360 A052823 A073817 A074048.)

Received June 20 2010; revised version received February 2 2011. Published in Journal of Integer Sequences, February 20 2011.

Return to Journal of Integer Sequences home page