{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,12]],"date-time":"2024-09-12T16:34:57Z","timestamp":1726158897724},"reference-count":39,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2022,2]]},"abstract":"<jats:p>In this paper, we carry out in an abstract order context some real subset combinatorial problems. Specifically, let [Formula: see text] be a finite poset, where [Formula: see text] is an order-reversing and involutive map such that [Formula: see text] for each [Formula: see text]. Let [Formula: see text] be the Boolean lattice with two elements and [Formula: see text] the family of all the order-preserving 2-valued maps [Formula: see text] such that [Formula: see text] if [Formula: see text] for all [Formula: see text]. In this paper, we build a family [Formula: see text] of particular subsets of [Formula: see text], that we call [Formula: see text]-bases on [Formula: see text], and we determine a bijection between the family [Formula: see text] and the family [Formula: see text]. In such a bijection, a [Formula: see text]-basis [Formula: see text] on [Formula: see text] corresponds to a map [Formula: see text] whose restriction of [Formula: see text] to [Formula: see text] is the smallest 2-valued partial map on [Formula: see text] which has [Formula: see text] as its unique extension in [Formula: see text]. Next we show how each [Formula: see text]-basis on [Formula: see text] becomes, in a particular context, a sub-system of a larger system of linear inequalities, whose compatibility implies the compatibility of the whole system.<\/jats:p>","DOI":"10.1142\/s0218196722500060","type":"journal-article","created":{"date-parts":[[2021,11,22]],"date-time":"2021-11-22T16:07:17Z","timestamp":1637597237000},"page":"127-157","source":"Crossref","is-referenced-by-count":1,"title":["Real subset sums and posets with an involution"],"prefix":"10.1142","volume":"32","author":[{"given":"Cinzia","family":"Bisi","sequence":"first","affiliation":[{"name":"Dipartimento di Matematica e Informatica, Universit\u00e1 di Ferrara, Via Machiavelli 30, 44121, Ferrara, Italy"}]},{"given":"Giampiero","family":"Chiaselotti","sequence":"additional","affiliation":[{"name":"Dipartimento di Matematica, Universit\u00e1 della Calabria, Via Pietro Bucci, Cubo 30B, 87036 Arcavacata di Rende (CS), Italy"}]},{"given":"Tommaso","family":"Gentile","sequence":"additional","affiliation":[{"name":"Dipartimento di Matematica, Universit\u00e1 della Calabria, Via Pietro Bucci, Cubo 30B, 87036 Arcavacata di Rende (CS), Italy"}]}],"member":"219","published-online":{"date-parts":[[2021,11,22]]},"reference":[{"key":"S0218196722500060BIB001","doi-asserted-by":"publisher","DOI":"10.1023\/A:1013900205912"},{"key":"S0218196722500060BIB002","doi-asserted-by":"publisher","DOI":"10.1155\/2015\/594294"},{"key":"S0218196722500060BIB003","first-page":"22","volume":"347","author":"Aledo J. 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