wildberger2. 132KB Jun 04 2011 12:09:42 AM
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In this Note we give elementary proofs – based on umbral calculus – of the most fundamental congruences satisfied by the Bell numbers and polynomials.. In particular, we establish
Carlitz, Generalized Stirling numbers, Combinatorial Analysis Notes , Duke University (1968), 8–15.
We give a greedy algorithm for describing an enumeration of the set of all natural numbers such that the sum of the first n terms of the sequence is divisible by n for each
The converse is also studied: given an SDD matrix C with the structure of a k -subdirect sum and positive diagonal entries, it is shown that there are two SDD matrices whose
As the main result (Theo- rem 3.1), we give a complete solution of Problem 1.1 in the case when the eigenvalues of the matrix (1.2) belong to F , and F is an infinite field..
To avoid infinite eigenvalues, we restrict ourselves to matrix polynomials with nonsingular leading coefficients.. The case of singular leading coefficients and infinite
We present the trigonometric Lax matrix and classical r -matrix for the Kowa- levski gyrostat on so (4) algebra by using the auxiliary matrix algebras so (3 , 2) or sp (4).. Key
Give the description of all irreducible configurations (associated with a fixed graph Γ and an arrangement of numbers on its edges) up to a unitary transformation.... We enumerate
