A simple explicit bijection between (n, 2) Gog and Magog trapezoids

Jérémie Bettinelli (1)

1 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]

A sub-problem of the open problem of finding an explicit bijection between alternating sign matrices and totally symmetric self-complementary plane partitions consists in finding an explicit bijection between so-called (n, k) Gog trapezoids and (n, k) Magog trapezoids. A quite involved bijection was found by Biane and Cheballah in the case k = 2. We give here a simpler bijection for this case.

Mots clés: Magog; Gog; alternating sign matrix; totally symmetric self-complementary plane partition; bijection

Domaines: Probabilités [math.PR]; Combinatoire [math.CO]

Jérémie Bettinelli. A simple explicit bijection between (n, 2) Gog and Magog trapezoids. Seminaire Lotharingien de Combinatoire, 2016, 75 (Art. B75e), pp.1--9. ⟨hal-01241820⟩