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5 papers · 2 filters
Symmetric chain decompositions of B_n and Pi_n
Erensto Damiani, Ottavio D'Antona, Daniel E. Loeb
We review the Green/Kleitman/Leeb interpretation of de Bruijn's symmetric chain decomposition of , and explain how it can be used to find a maximal collection of disj…
A new proof of Monjardet's median theorem
Daniel E. Loeb
New proofs are given for Monjardet's theorem that all strong simple games (i.e., ipsodual elements of the free distributive lattice) can be generated by the median operation. Tight…
A generalization of the binomial coefficients
Daniel E. Loeb
We pose the question of what is the best generalization of the factorial and the binomial coefficient. We give several examples, derive their combinatorial properties, and demonstr…
Series with general exponents
Daniel E. Loeb
We define the Artinian and Noetherian algebra which consist of formal series involving exponents which are not necessarily integers. All of the usual operations are defined here an…
A simpler characterization of Sheffer polynomial
Alessandro Di Bucchianico, Daniel E. Loeb
We characterize the Sheffer sequences by a single convolution identity where is a shift-invariant operator.…