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# Combinatorics of the Heat Trace on Spheres

Published:2002-10-01
Printed: Oct 2002
• Iosif Polterovich
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## Abstract

We present a concise explicit expression for the heat trace coefficients of spheres. Our formulas yield certain combinatorial identities which are proved following ideas of D.~Zeilberger. In particular, these identities allow to recover in a surprising way some known formulas for the heat trace asymptotics. Our approach is based on a method for computation of heat invariants developed in [P].
 MSC Classifications: 05A19 - Combinatorial identities, bijective combinatorics 58J35 - Heat and other parabolic equation methods