@inproceedings{415e1838716d42a687ebc46c9cb61076,
title = "Bipartite perfect matching as a real polynomial",
abstract = "We obtain a description of the Bipartite Perfect Matching decision problem as a multilinear polynomial over the Reals. We show that it has full degree and (1-on(1))· 2n2 monomials with non-zero coefficients. In contrast, we show that in the dual representation (switching the roles of 0 and 1) the number of monomials is only exponential in I(n logn). Our proof relies heavily on the fact that the lattice of graphs which are {"}matching-covered{"}is Eulerian.",
keywords = "Bipartite Perfect Matching, Boolean Functions, Elementary Graphs",
author = "Gal Beniamini and Noam Nisan",
note = "Publisher Copyright: {\textcopyright} 2021 ACM.; 53rd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2021 ; Conference date: 21-06-2021 Through 25-06-2021",
year = "2021",
month = jun,
day = "15",
doi = "10.1145/3406325.3451002",
language = "الإنجليزيّة",
series = "Proceedings of the Annual ACM Symposium on Theory of Computing",
pages = "1118--1131",
editor = "Samir Khuller and Williams, \{Virginia Vassilevska\}",
booktitle = "STOC 2021 - Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing",
}