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Stack-Sortable Permutations and Polynomials
Catalan numbers stack-sortable permutations permutations acting on polynomials
2010/2/25
The Catalan numbers show up in a diverse variety of counting problems. In this note we give yet another characterization of the Catalan number C(n). It is characterized as the dimension of a certain s...
Valuations of Polynomials
Polynomials valuations of polynomials Order Condition Algebraic Subpolynomial Condition Subpolynomial Condition
2010/2/26
A tree is a connected (undirected) graph that contains no cycles. Trees play an important role in Computer Science. There are many applications in this field. Ordered binary decision diagrams are tree...
Fermionic formulas for level-restricted generalized Kostka polynomials and coset branching functions
Fermionic formulas Kostka polynomials coset branching functions
2010/10/29
Level-restricted paths play an important role in crystal theory. They correspond to certain highest weight vectors of modules of quantum affine algebras. We show that the recently established bijecti...
Parity considerations in the expansion of Fermat-Pell polynomials
Parity considerations expansion Fermat-Pell polynomials
2010/11/1
For each positive integer $n$ it is shown how to construct a finite collection of multivariable polynomials $\{F_{i}:=F_{i}(t,X_{1},..., X_{\lfloor \frac{n+1}{2} \rfloor})\}$ such that each positive ...
