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A solution in this class can be expressed as a sum of exponentials, and we look at combinations of signs (signatures) for the nonvanishing terms in this sum. We prove a characterization of the signatures that return another solution of the KP II equation: they can be represented as choices of signs for columns and rows of a coefficient matrix, so we recover a function satisfying the whole KP hierarchy from this single constraint. The redundancy of this representation for different choices of the initial solution is investigated. Enumerative, information-theoretic, and geometric aspects of this construction are discussed.<\/jats:p>","DOI":"10.1063\/1.5086165","type":"journal-article","created":{"date-parts":[[2019,7,31]],"date-time":"2019-07-31T14:55:20Z","timestamp":1564584920000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":4,"title":["Complexity reduction for sign configurations through the KP II equation and its information-theoretic aspects"],"prefix":"10.1063","volume":"60","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9782-7834","authenticated-orcid":false,"given":"Mario","family":"Angelelli","sequence":"first","affiliation":[{"name":"Department of Mathematics and Physics \u201cEnnio De Giorgi,\u201d University of Salento and Sezione INFN , 73100 Lecce, Italy"}]}],"member":"317","published-online":{"date-parts":[[2019,7,31]]},"reference":[{"key":"2023070118130923500_c1","doi-asserted-by":"publisher","first-page":"112","DOI":"10.1016\/j.geomphys.2017.04.005","article-title":"On a family of KP multi-line solitons associated to rational degenerations of real hyperelliptic curves and to the finite non-periodic Toda hierarchy","volume":"119","year":"2017","journal-title":"J. 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