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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...
A method for determining the mod-$2^k$ behaviour of recursive sequences, with applications to subgroup counting
Polynomial recurrences symbolic summation subgroup numbers free subgroup numbers Catalan numbers
2011/9/1
Abstract: We present a method to obtain congruences modulo powers of 2 for sequences given by recurrences of finite depth with polynomial coefficients. We apply this method to Catalan numbers, Fu\ss-C...
Series expansions from the corner transfer matrix renormalization group method: the hard squares model
Corner transfer matrix hard squares model series expansions
2011/9/30
Abstract: The corner transfer matrix renormalization group method is an efficient method for evaluating physical quantities in statistical mechanical models. It originates from Baxter's corner transfe...
Proofs of some binomial identities using the method of last squares
binomial identities method of last squares Proofs Combinatorics
2011/8/26
Abstract: We give combinatorial proofs for some identities involving binomial sums that have no closed form.
A method for constructing random matrix models of disordered bosons
random matrix models disordered bosons
2011/2/22
Random matrix models of disordered bosons consist of matrices in the Lie algebra g = spn(R). Assuming dynamical stability, their eigenvalues are required to be purely imaginary.