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Real subset sums and posets with an involution
- Source :
- International Journal of Algebra and Computation. 32:127-157
- Publication Year :
- 2021
- Publisher :
- World Scientific Pub Co Pte Ltd, 2021.
-
Abstract
- 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.
- Subjects :
- Computer Science::Information Retrieval
General Mathematics
Carry (arithmetic)
Astrophysics::Instrumentation and Methods for Astrophysics
Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing)
Context (language use)
Combinatorics
TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES
ComputingMethodologies_DOCUMENTANDTEXTPROCESSING
Computer Science::General Literature
Order (group theory)
Involution (philosophy)
Partially ordered set
ComputingMilieux_MISCELLANEOUS
Mathematics
Subjects
Details
- ISSN :
- 17936500 and 02181967
- Volume :
- 32
- Database :
- OpenAIRE
- Journal :
- International Journal of Algebra and Computation
- Accession number :
- edsair.doi...........dadec75c2eebd23f711a5fa57fe0637a