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Mémoire Sur Les Probabilités∗

I intend to treat in this Memoir two important points in the analysis of chances which do not seem yet to have been sufficiently deeply studied: the first has for object the manner of calculating the probability of events composed of simple events of which one does not know the respective probabilities; the object of the second is the influence of past events on the probability of future events...

Mémoire Sur Les Suites

The theory of series is one of the most important objects of Analysis: all problems which reduce to some approximations, and consequently nearly all the applications of Mathematics to Nature, depend on this theory; thus we see that it has principally fixed the attention of the geometers; they have found a great number of beautiful theorems and ingenious methods, either in order to expand functi...

Une note sur les contractions dans les polygones orthogonaux

Maire, F., Une note sur les contractions dans les polygones orthogonaux, Discrete Mathematics 111 (1993) 3677371. We define a contraction for orthogonal polygons, and show that such a polygon can be transformed into a rectangle by a sequence of contractions. This result gives a new proof of the orthogonal art gallery theorem. We present also a property of the maximal rectangles contained in ort...

Opérades différentielles graduées sur les simplexes et les permutoèdres

We define several differential graded operads, some of them being related to families of polytopes : simplices and permutohedra. We also obtain a presentation by generators and relations of the operad K on associahedra introduced in a previous article.

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