
EVERY POSITIVE K-BONACCI-LIKE SEQUENCE EVENTUALLY
... If we are dealing with the Fibonacci numbers (k = 2), the support of d is [0, 1], and Z(d) = d(1) and Z(Sd) = d(0) + d(1). Appropriate choices of d(0) and d(1) can give any desired values for Z(d) and Z(Sd). If we are dealing with the tribonacci numbers (k = 3), the support of d is [−1, 0, 1], and Z ...
... If we are dealing with the Fibonacci numbers (k = 2), the support of d is [0, 1], and Z(d) = d(1) and Z(Sd) = d(0) + d(1). Appropriate choices of d(0) and d(1) can give any desired values for Z(d) and Z(Sd). If we are dealing with the tribonacci numbers (k = 3), the support of d is [−1, 0, 1], and Z ...
Full text
... is, without a hypothesis on N(x), and it is those I am concerned with here* Those needing a hypothesis on N(x) , I assume included in §2. However, the fact that the g.i, can be ordered and so a counting function N(x) exists, is important. Since there will now be a slight change in notation, I will r ...
... is, without a hypothesis on N(x), and it is those I am concerned with here* Those needing a hypothesis on N(x) , I assume included in §2. However, the fact that the g.i, can be ordered and so a counting function N(x) exists, is important. Since there will now be a slight change in notation, I will r ...
A Combinatorial Miscellany
... the Notes section points to some more general accounts that can help remedy this shortcoming. With some simplification, combinatorics can be said to be the mathematics of the finite. One of the most basic properties of a finite collection of objects is its number of elements. For instance, take word ...
... the Notes section points to some more general accounts that can help remedy this shortcoming. With some simplification, combinatorics can be said to be the mathematics of the finite. One of the most basic properties of a finite collection of objects is its number of elements. For instance, take word ...
Densities and derivatives - Department of Statistics, Yale
... For example, if µ is Lebesgue measure on B(R), the probability measure defined by the density (x) = (2π )−1/2 exp(−x 2 /2) with respect to µ is called the standard normal distribution, usually denoted by N (0, 1). If µ is counting measure on N0 (that is, mass 1 at each nonnegative integer), the pro ...
... For example, if µ is Lebesgue measure on B(R), the probability measure defined by the density (x) = (2π )−1/2 exp(−x 2 /2) with respect to µ is called the standard normal distribution, usually denoted by N (0, 1). If µ is counting measure on N0 (that is, mass 1 at each nonnegative integer), the pro ...
RISES, LEVELS, DROPS AND - California State University, Los
... [7], meets between subsets of a lattice [3], and alternating sign matrices [4], to name just a few. Alladi and Hoggatt also derived results about the number of times a ...
... [7], meets between subsets of a lattice [3], and alternating sign matrices [4], to name just a few. Alladi and Hoggatt also derived results about the number of times a ...
Sequences
... the Secret Service assigns a code name to the president of the United States and the first family. Some classic code names for former U.S. presidents were “Tumbler” for President George Walker Bush, “Timberwolf” for President George Herbert Walker Bush, “Deacon” for President Jimmy Carter, and “Lanc ...
... the Secret Service assigns a code name to the president of the United States and the first family. Some classic code names for former U.S. presidents were “Tumbler” for President George Walker Bush, “Timberwolf” for President George Herbert Walker Bush, “Deacon” for President Jimmy Carter, and “Lanc ...
Total recursive functions that are not primitive recursive
... recursive. Sudan published the lesser-known Sudan function, then shortly afterwards and independently, in 1928, Ackermann published his function ϕ. Ackermann’s three-argument function, ϕ(m, n, p), is defined such that for p = 0, 1, 2, it reproduces the basic operations of addition, multiplication, a ...
... recursive. Sudan published the lesser-known Sudan function, then shortly afterwards and independently, in 1928, Ackermann published his function ϕ. Ackermann’s three-argument function, ϕ(m, n, p), is defined such that for p = 0, 1, 2, it reproduces the basic operations of addition, multiplication, a ...
Sheffer sequences, probability distributions and approximation
... Taylor expansion of polynomials is a special case of (5) where sk (x) = xk /k! and thus Q = D and S = I. Moreover, (6) with the same choice yields that each shift-invariant operator can be expanded into a power series in D. Note that there are no convergence problems, since all infinite sums reduce ...
... Taylor expansion of polynomials is a special case of (5) where sk (x) = xk /k! and thus Q = D and S = I. Moreover, (6) with the same choice yields that each shift-invariant operator can be expanded into a power series in D. Note that there are no convergence problems, since all infinite sums reduce ...