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The set of Dyck paths of length $2n$ inherits a lattice structure from a bijection with the set of noncrossing partitions with the usual partial order. In this paper, we study the joint distribution o...
We present a new approach for counting trees, and we apply it to count multitype Cayley trees and to prove the multivariate Lagrange inversion formula. The gist of our approach is to exploit the symme...
Counting independent sets of a fixed size in graphs with a given minimum degree
graphs given minimum degree independent sets Combinatorics
2012/4/16
Galvin showed that for all fixed $\delta$ and sufficiently large $n$, the $n$-vertex graph with minimum degree $\delta$ that admits the most independent sets is the complete bipartite graph $K_{\delta...
Computational and Theoretical Challenges on Counting Solid Standard Young Tableaux
Computational Theoretical Challenges Counting Solid Standard Young Tableaux
2012/2/29
In how many ways can you place n chocolate pieces all of different sizes in an n by n chocolate box, in such a way that when you go from left to right and from top to bottom, there are no gaps AND the...
On the functions counting walks with small steps in the quarter plane
Walks in the quarter plane counting generating function holonomy group of the walk Riemann surface elliptic functions
2011/9/5
Abstract: Models of spatially homogeneous walks in the quarter plane with steps taken from the eight nearest neighbors are considered. Counting function $(x,y,z)\mapsto Q(x,y;z)$ of the numbers $q(i,j...
A method for determining the mod-$2^k$ behaviour of recursive sequences, with applications to subgroup counting
Polynomial recurrences symbolic summation subgroup numbers free subgroup numbers Catalan numbers
2011/9/1
Abstract: We present a method to obtain congruences modulo powers of 2 for sequences given by recurrences of finite depth with polynomial coefficients. We apply this method to Catalan numbers, Fu\ss-C...
Counting in Graph Covers: A Combinatorial Characterization of the Bethe Entropy Function
Graph Covers Combinatorial Characterization Bethe Entropy Function
2011/1/14
We present a combinatorial characterization of the Bethe entropy function of a factor graph, such a characterization being in contrast to the original, analytical, definition of this
function. We ach...
Counting SO(9)xSU(2) representations in coordinate independent state space of SU(2) Matrix Theory
Counting SO(9)xSU(2) representations SU(2) Matrix Theory
2010/12/8
We consider decomposition of coordinate independent states into SO(9)×SU(2)representations in SU(2) Matrix theory. To see what and how many representations appear in the decomposition, we compute the ...