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On the volume of lattice manifolds

Published online by Cambridge University Press:  17 April 2009

Krzysztof Kołodziejczyk
Krzysztof Kołodziejczyk
Affiliation:
Institute of Mathematics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland e-mail: kolodz@im.pwr.wroc.pl
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Abstract

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The volume of a general lattice polyhedron P in ℝN can be determined in terms of numbers of lattice points from N − 1 different lattices in P Ehrhart gave a formula for the volume of “polyèdre entier” in even-dimensional spaces involving only N/2 lattices. The aim of this note is to comment on Ehrhart's formula and provide a similar volume formula applicable to lattice polyhedra that are N-dimensional manifolds in ℝN.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 61 , Issue 2 , April 2000 , pp. 313 - 318
Copyright
Copyright © Australian Mathematical Society 2000

References

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