Shoma Fujino

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math.CT2022

Lovàsz's hom-counting theorem by inclusion-exclusion principle

Shoma Fujino, Makoto Matsumoto

Let $C$ be the category of finite graphs. Lovàsz (1967) shows that if $∣ Hom (X, A) ∣ = ∣ Hom (X, B) ∣$ holds for any $X$ , then $A$ is isomorphic to $B$ . Pultr (…

math.CT2022

Locally-finite extensive categories, their semi-rings, and decomposition to connected objects

Shoma Fujino, Makoto Matsumoto

Let $C$ be the category of finite graphs. Lovàsz shows that the semi-ring of isomorphism classes of $C$ (with coproduct as sum, and product as multiplication) is…