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On symmetric structures of order two

Abstract : Let (w_n)0 < n be the sequence known as Integer Sequence A047749 In this paper, we show that the integer w_n enumerates various kinds of symmetric structures of order two. We first consider ternary trees having a reflexive symmetry and we relate all symmetric combinatorial objects by means of bijection. We then generalize the symmetric structures and correspondences to an infinite family of symmetric objects.
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Michel Bousquet, Cédric Lamathe. On symmetric structures of order two. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2008, Vol. 10 no. 2 (2), pp.153--176. ⟨10.46298/dmtcs.420⟩. ⟨hal-00972316⟩

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