A recursive approach for the enumeration of the homomorphisms from a poset P to the chain C₃

2021/04/07 by Frank a Campo, Campo, Frank a
Mathematics · #06A07 (Primary) 06A06 (Secondary) #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2104.03079

openalex publication_date 2021/04/07 · openalex created_date 2021/04/13 · openalex updated_date 2026/07/28

Abstract

Let \cal H(P,C₃) be the set of order homomorphisms from a poset P to the chain C₃ = 1 < 2 < 3. We develop a recursive approach for the calculation of the cardinality of \cal H(P,C₃), and we apply it on several types of posets, including P = C₃ × C₃ × C_k and P = \cal H(C_k, C₃); for the latter poset P, we derive a direct formula for # \cal H ( P, C₃ ).

Citations

• Doppelgangers: the Ur-Operation and Posets of Bounded Height

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