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Permutations defining convex permutominoes.
A permutomino of size n is a polyomino determined by particular pairs (�1,�2) of permutations of size n, such that �1(i) 6 �2(i), for 1 ≤ i ≤ n. Here we determine
Some Statistics on the Hypercubes of Catalan Permutations
- F. Disanto
- Mathematics, Computer ScienceJ. Integer Seq.
The graph Qn(σ) is obtained by imposing edge constraints on the classical oriented hypercube Qn, such that each path going from 0 to 1 in Qn (σ) bijectively encodes a permutation of size n avoiding the pattern σ.
Exact enumeration of cherries and pitchforks in ranked trees under the coalescent model.
Monte Carlo modeling of the dual-mode regime in quantum-well and quantum-dot semiconductor lasers.
A possible steady-state dual-mode regime is predicted for specially designed QD semiconductor lasers thereby acting as a CW microwave or terahertz-beating source whereas it does not occur for QW lasers.
Yule-generated trees constrained by node imbalance.
A Closed Formula for the Number of Convex Permutominoes
A closed formula is determined for the number of convex permutominoes of size $n+1$ by providing a recursive generation of all convex permits of size n from the objects of sizen, according to the ECO method, and translating this construction into a system of functional equations satisfied by the generating function of conveX permutOMinoes.
Catalan pairs: A relational-theoretic approach to Catalan numbers
Enumeration of Ancestral Configurations for Matching Gene Trees and Species Trees
This work studies ancestral configurations in balanced and unbalanced families of trees determined by a given seed tree, showing that for seed trees with more than one taxon, the number of ancestral configurations increases for both families exponentially in the numberof taxa n.
Coalescent Histories for Lodgepole Species Trees
The number of coalescent histories for the lodgepole species trees is determined, in the case that the gene tree matches the species tree, showing that this number grows with m!! in the number of taxa m.
Dual-wavelength laser for THz generation by photo-mixing
We present the design and the fabrication of a dual-wavelength micro-photonic resonator combining a photonic crystal membrane (PCM) and a vertical Fabry Perot (FP) cavity where the former is embedded…