Limiting Distribution of Frobenius Numbers for N = 3

Viewing Some Ordinary Differential Equations from the Angle of Derivative Polynomials

In the paper, the authors view some ordinary differential equations and their solutions from the angle of (the generalized) derivative polynomials and simplify some known identities for the Bernoulli numbers and polynomials, the Frobenius-Euler polynomials, the Euler numbers and polynomials, in terms of the Stirling numbers of the first and second kinds.

Compact Suffix Trees Resemble PATRICIA Tries: Limiting Distribution of the Depth

Suffix trees are the most frequently used data structures in algorithms on words. In this paper, we consider the depth of a compact suffix tree, also known as the PAT tree, under some simple probabilistic assumptions. For a biased memoryless source, we prove that the limiting distribution for the depth in a PAT tree is the same as the limiting distribution for the depth in a PATRICIA trie, even...

Limiting behaviour of large Frobenius numbers

Exact Properties of Frobenius Numbers and Fraction of the Symmetric Semigroups in the Weak Limit for N=3

We generalize and prove a hypothesis by V. Arnold on the parity of Frobenius number. For the case of symmetric semigroups with three generators of Frobenius numbers we found an exact formula, which in a sense is the sum of two Sylvester’s formulaes. We prove that the fraction of the symmetric semigroups is vanishing in the weak limit. 1. Definitions Take n mutually prime numbers a1, a2, ..., an...

Euler–frobenius Numbers and Rounding

We study the Euler–Frobenius numbers, a generalization of the Eulerian numbers, and the probability distribution obtained by normalizing them. This distribution can be obtained by rounding a sum of independent uniform random variables; this is more or less implicit in various results and we try to explain this and various connections to other areas of mathematics, such as spline theory. The mea...