Polynomial Sequences of Binomial Type Path Integrals

2002 ◽  
Vol 6 (1) ◽  
pp. 45-56 ◽  
Author(s):  
Vladimir V. Kisil
Keyword(s):  
Path Integrals ◽  
Polynomial Sequences ◽  
Binomial Type

scholarly journals Polynomial Sequences of Binomial-Type Arising in Graph Theory

10.37236/3702 ◽  
2014 ◽  
Vol 21 (1) ◽  
Author(s):  
Jonathan Schneider
Keyword(s):  
Graph Theory ◽  
Large Class ◽  
Higher Dimensions ◽  
Polynomial Sequence ◽  
Chromatic Polynomials ◽  
Grid Graphs ◽  
Polynomial Sequences ◽  
Fixed Set ◽  
Binomial Type ◽  
Open Question

In this paper, we show that the solution to a large class of "tiling'' problems is given by a polynomial sequence of binomial type. More specifically, we show that the number of ways to place a fixed set of polyominos on an $n\times n$ toroidal chessboard such that no two polyominos overlap is eventually a polynomial in $n$, and that certain sets of these polynomials satisfy binomial-type recurrences. We exhibit generalizations of this theorem to higher dimensions and other lattices. Finally, we apply the techniques developed in this paper to resolve an open question about the structure of coefficients of chromatic polynomials of certain grid graphs (namely that they also satisfy a binomial-type recurrence).

Path integrals and the solution of the Schwinger model in curved space-time

1986 ◽  
Vol 33 (8) ◽  
pp. 2262-2266 ◽  
Author(s):  
J. Barcelos-Neto ◽  
Ashok Das
Keyword(s):  
Path Integrals ◽  
Space Time ◽  
Curved Space ◽  
Schwinger Model

Unbiased Simulation Estimators for Path Integrals of Diffusions

2020 ◽  
Author(s):  
Guanting Chen ◽  
Alex Shkolnik ◽  
Kay Giesecke
Keyword(s):  
Path Integrals
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