Bipartition orders and statistics on words. (Ordres bipartitionnaires et statistiques sur les mots.)
A geometric version of the Kerov-Kirillov-Reshetikhin construction. (Une version géométrique de la construction de Kerov-Kirilov-Reshetikhin.)
Discovering hook length formulas by an expansion technique.
The triple, quintuple and setuple product identities revisited.
Unavoidable sets. (Ensembles inévitables.)
The -analogs of secant and tangent numbers.
Basic calculus of signed permutations. II: Finite analogues of Bessel functions. (Calcul basique des permutations signées. II: Analogues finis des fonctions de Bessel.)
Inverses of words.
Signed words and permutations. II: The Euler-Mahonian polynomials.
Signed words and permutations. III: The MacMahon Verfahren.
Decreases and descents in words.
Rectangular Scott-type permanents.
The hyperharmonic numbers and the phratry of the coupon collector. (Les nombres hyperharmoniques et la fratrie du collectionneur de vignettes.)
The Nekrasov-Okounkov hook length formula: refinement, elementary proof, extension and applications
The paper is devoted to the derivation of the expansion formula for the powers of the Euler Product in terms of partition hook lengths, discovered by Nekrasov and Okounkov in their study of the Seiberg-Witten Theory. We provide a refinement based on a new property of -cores, and give an elementary proof by using the Macdonald identities. We also obtain an extension by adding two more parameters, which appears to be a discrete interpolation between the Macdonald identities and the generating function...
Secant tree calculus
A true Tree Calculus is being developed to make a joint study of the two statistics “eoc” (end of minimal chain) and “pom” (parent of maximum leaf) on the set of secant trees. Their joint distribution restricted to the set {eoc-pom ≤ 1} is shown to satisfy two partial difference equation systems, to be symmetric and to be expressed in the form of an explicit three-variable generating function.
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