Journal of Combinatorics

Volume 9 (2018)

Number 1

Graded Betti numbers of cycle graphs and standard Young tableaux

Pages: 1 – 7



Steven Klee (Department of Mathematics, Seattle University, Seattle, Washington, U.S.A.)

Matthew T. Stamps (Division of Science, Yale-NUS College, Singapore)


We give a bijective proof that the graded Betti numbers of a minimal free resolution of the Stanley–Reisner ring of a cycle graph (viewed as a one-dimensional simplicial complex) are given by the number of standard Young tableaux of a given shape.

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This work was supported in part by NSF Grant #1159206.

Received 21 April 2015

Published 5 January 2018