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A Method for Obtaining Generating Function for Central Coefficients of Triangles
Obtaining Generating Function Central Coefficients of Triangles Combinatorics
2012/6/21
We consider problems of obtaining a generating function for the central coefficients of triangle $T(n,k)$, which is given by expression $[xG(x)]^k=\sum_{n\geqslant k} T(n,k)x^n$, $G(0)\neq 0$. We prov...
The Mobius function of generalized subword order
Chebyshev polynomial discrete Morse theory homotopy type minimal skipped interval Mobius function
2011/9/20
Abstract: Let P be a poset and let P* be the set of all finite length words over P. Generalized subword order is the partial order on P* obtained by letting u \le w if and only if there is a subword u...
Spanning trees and expansions for the Potts model partition function in an external field
Tutte polynomial Potts model spanning trees V -polynomial external field Hamiltonian edge activities
2011/9/5
Abstract: We use a deletion-contraction relation for the variable field Potts model partition function to give an expansion of the variable field Potts model partition function in terms of the zero fi...
Counting in Graph Covers: A Combinatorial Characterization of the Bethe Entropy Function
Graph Covers Combinatorial Characterization Bethe Entropy Function
2011/1/14
We present a combinatorial characterization of the Bethe entropy function of a factor graph, such a characterization being in contrast to the original, analytical, definition of this
function. We ach...
Equilibrium states of the pressure function for products of matrices
pressure function products of matrices
2010/12/7
Let {Mi}ℓ i=1 be a non-trivial family of d × d complex matrices, in the sense that for any n ∈ N, there exists i1 · · · in ∈ {1, . . . , ℓ}n such that Mi1 · · ·Min 6= 0. Let P: (0,∞) → R b...