scholarly journals Schur type functions associated with polynomial sequences of binomial type

2008 ◽  
Vol 14 (2) ◽  
pp. 247-274
Author(s):  
Minoru Itoh
Keyword(s):  
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).

The Almost Orthogonal Polynomial Sequences

2010 ◽  
Author(s):  
M. S. Stanković ◽  
B. Danković ◽  
S. Marinković ◽  
P. M. Rajković ◽  
Michail D. Todorov ◽  
...  
Keyword(s):  
Orthogonal Polynomial ◽  
Polynomial Sequences

On the Symmetric H q -Semiclassical Polynomial Sequences of Even Class. Some Examples from the Class Two

2012 ◽  
Vol 10 (3) ◽  
pp. 1293-1316
Author(s):  
Mohamed Ihsen Tounsi ◽  
Imed Ben Salah ◽  
Lotfi Khriji
Keyword(s):  
Polynomial Sequences
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