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Preprint Number 1893
1893. Esther Elbaz Saban Grothendieck ring of the pairing function without cycles E-mail: Submission date: 11 December 2020 Abstract: A bijection (l,r) between M^2 and M is said to be a pairing function with no cycles, if any composition of its coordinate functions has no fixed point. We compute here the Grothendieck ring of the pairing function without cycles to be isomorphic to ℤ^2 ≃ ℤ[X]/(X-X^2). More generally, for any n in ℕ^* and any bijetion without cycles betwen M and M^n, the exact same method proves that K_0(M)=ℤ[X]/(X-X^n). Mathematics Subject Classification: Primary 03C07, Secondary 03C10, 03C98, 08C10 Keywords and phrases: |
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