scholarly journals New Characteristics of Some Polynomial Sequences in Combinatorial Theory

1993 ◽  
Vol 175 (1) ◽  
pp. 199-205 ◽  
Author(s):  
X.H. Sun
Keyword(s):  
Combinatorial Theory ◽  
Polynomial Sequences

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

scholarly journals A Compositional Shuffle Conjecture Specifying Touch Points of the Dyck Path

2012 ◽  
Vol 64 (4) ◽  
pp. 822-844 ◽  
Author(s):  
J. Haglund ◽  
J. Morse ◽  
M. Zabrocki
Keyword(s):  
Building Blocks ◽  
Main Diagonal ◽  
Combinatorial Theory ◽  
Dyck Path ◽  
Dyck Paths ◽  
Littlewood Polynomials ◽  
Diagonal Harmonics ◽  
Littlewood Polynomial ◽  
Theory Operator ◽  
Shuffle Conjecture

Abstract We introduce a q, t-enumeration of Dyck paths that are forced to touch the main diagonal at specific points and forbidden to touch elsewhere and conjecture that it describes the action of the Macdonald theory ∇ operator applied to a Hall–Littlewood polynomial. Our conjecture refines several earlier conjectures concerning the space of diagonal harmonics including the “shuffle conjecture” (Duke J. Math. 126 (2005), pp. 195 − 232) for ∇ en[X]. We bring to light that certain generalized Hall–Littlewood polynomials indexed by compositions are the building blocks for the algebraic combinatorial theory of q, t-Catalan sequences, and we prove a number of identities involving these functions.

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