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The facets of the matroid polytope and the independent set polytope of a positroid
A positroid is a special case of a realizable matroid, that arose from the study of totally nonnegative part of the Grassmannian by Postnikov. Postnikov demonstrated that positroids are in bijectionExpand
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Elementary analysis of isolated zeroes of a polynomial system
Wooley (J. Number Theory, 1996) gave an elementary proof of a Bezout like theorem allowing one to count the number of isolated integer roots of a system of polynomial equations modulo some primeExpand
O ct 2 01 9 A Self-contained Analysis of the Lempel-Ziv Compression Algorithm Madhu Sudan
This article gives a self-contained analysis of the performance of the Lempel-Ziv compression algorithm on (hidden) Markovian sources. Specifically we include a full proof of the assertion that theExpand
A Self-contained Analysis of the Lempel-Ziv Compression Algorithm
TLDR
This article gives a self-contained analysis of the performance of the Lempel-Ziv compression algorithm on (hidden) Markovian sources. Expand
Flats of a positroid from its decorated permutation
A positroid is a special case of a realizable matroid, that arose from the study of totally nonnegative part of the Grassmannian by Postnikov. Postnikov demonstrated that positroids are in bijectionExpand
Decoding Concatenated Codes 2 Reed-Solomon Decoding
(2) Output WE . We claim that if the βi arise from an instance of Reed-Solomon encoding with fewer than t errors (i.e. there is some polynomial M with degree less than k such that M(αi) = βi for atExpand
Flats of a positroid
A nonuniform Littlewood-Offord inequality for all norms
Let $\mathbf{v}_i$ be vectors in $\mathbb{R}^d$ and $\{\varepsilon_i\}$ be independent Rademacher random variables. Then the Littlewood-Offord problem entails finding the best upper bound forExpand