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Bell and Stirling Numbers for Graphs
The Bell number B(G) of a simple graph G is the number of partitions of its vertex set whose blocks are independent sets of G. The number of these partitions with k blocks is the (graphical) StirlingExpand
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Hausdorff Dimension in Pascal’s Triangle
One of the easiest and best known ways to generate a self-similar fractal pattern is to view from an infinite distance the set of lattice points (m, k) for which ( m k ) is odd. More generally, oneExpand
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Matrix Powers of Column-Justified Pascal Triangles and Fibonacci Sequences
If L, respectively R are matrices with entries binom{i-1,j-1}, respectively binom{i-1,n-j}, it is known that L^2 = I (mod 2), respectively R^3 = I (mod 2), where I is the identity matrix of dimensionExpand
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On finite partition representations of lattices
  • R. Peele
  • Computer Science, Mathematics
  • Discret. Math.
  • 1982
TLDR
It was recently proved by Pudlak and Tuma that every finite lattice L can be represented as a sublattice of a finite partition lattice E(V). Expand
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Some Counting Problems Involving the Multinomial Expansion
One of the loveliest and most surprising results of elementary number theory is Kummer's carry theorem. In the generalized form in which we will apply it, it says that for any nonnegative integersExpand
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Fractal patterns derived from rational binomial coefficients
It is known (e.g., [11]) that for p prime and e ∈ ℤ ≥, the array of integer lattice points (x,y) such that 0 ≤ y ≤ x and (x y) is exactly divisible by p e , takes on a fractal-like appearance whenExpand
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N ov 2 00 0 Spectral Properties of a Binomial Matrix
(matrix Rn) and derived many interesting results on powers of these matrices. In [5], the author found that the same is true for a much larger class of what he called netted matrices, namely matricesExpand
A Carry Theorem for Rational Binomial Coefficients
Ernst Eduard Kummer proved in 1852 that for any nonnegative integers j and k and any prime p, the exponent of the highest power of p that divides the binomial coefficient \( \begin{array}{*{20}{c}}Expand
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