Syngenetic rapid growth of ellipsoidal silica concretions with bitumen cores

Isolated silica concretions in calcareous sediments have unique shapes and distinct sharp boundaries and are considered to form by diagenesis of biogenic siliceous grains. However, the details and rates of syngenetic formation of these spherical concretions are still not fully clear. Here we present a model for concretion growth by diffusion, with chemical buffering involving decomposition of organic matter leading to a pH change in the pore-water and preservation of residual bitumen cores in the concretions. The model is compatible with some pervasive silica precipitation. Based on the observed elemental distributions, C, N, S, bulk carbon isotope and carbon preference index (CPI) measurements of the silica-enriched concretions, bitumen cores and surrounding calcareous rocks, the rate of diffusive concretion growth during early diagenesis is shown using a diffusion-growth diagram. This approach reveals that ellipsoidal SiO2 concretions with a diameter of a few cm formed rapidly and the precipitated silica preserved the bitumen cores. Our work provides a generalized chemical buffering model involving organic matter that can explain the rapid syngenetic growth of other types of silica accumulation in calcareous sediments.

Modified Growth Diagrams, Permutation Pivots, and the BWX Map $\phi^*$

International audience In their paper on Wilf-equivalence for singleton classes, Backelin, West, and Xin introduced a transformation $\phi^*$, defined by an iterative process and operating on (all) full rook placements on Ferrers boards. Bousquet-Mélou and Steingrimsson proved the analogue of the main result of Backelin, West, and Xin in the context of involutions, and in so doing they needed to prove that $\phi^*$ commutes with the operation of taking inverses. The proof of this commutation result was long and difficult, and Bousquet-Mélou and Steingrimsson asked if $\phi^*$ might be reformulated in such a way as to make this result obvious. In the present paper we provide such a reformulation of $\phi^*$, by modifying the growth diagram algorithm of Fomin. This also answers a question of Krattenthaler, who noted that a bijection defined by the unmodified Fomin algorithm obviously commutes with inverses, and asked what the connection is between this bijection and $\phi^*$. Dans leur article sur l'équivalence de Wilf pour les classes de singletons, Backelin, West et Xin ont introduit une transformation $\phi^*$, définie par un processus itératif et opérant sur (tous) les placements complets de tours sur un plateau de Ferrers. Bousquet-Melou et Steingrimsson ont démontré l'analogue du résultat principal de Backelin, West et Xin dans le contexte d'involutions, et pour ce faire ont eu besoin de démontrer que $\phi^*$ commute avec l'opération inverse. La preuve de cette commutativité est longue et difficile, et Bousquet-Melou et Steingrômsson se demandèrent s'il n'était pas possible de reformuler $\phi^*$ de sorte que le resultat devienne évident. Dans le présent article, nous proposons une telle reformulation de $\phi^*$ en modifiant l'algorithme de croissance de diagramme de Fomin. Cette reformulation répond également à une question de Krattenthaler, qui, remarquant qu'une bijection définie par l'algorithme de Fomin non modifié commute évidemment avec l'opération inverse, se demanda quel était le rapport entre cette bijection et $\phi^*$.