A simple bijection for the regions of the Shi arrangement of hyperplanes
نویسندگان
چکیده
The Shi arrangement Sn is the arrangement of affine hyperplanes in R n of the form xi−xj = 0 or 1, for 1 ≤ i < j ≤ n. It dissects R n into (n+1) regions, as was first proved by Shi. We give a simple bijective proof of this result. Our bijection generalizes easily to any subarrangement of Sn containing the hyperplanes xi − xj = 0 and to the extended Shi arrangements.
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ورودعنوان ژورنال:
- Discrete Mathematics
دوره 204 شماره
صفحات -
تاریخ انتشار 1999