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Generalised quadrangles with a group of automorphisms acting primitively on points and lines
Generalised quadrangle primitive permutation group Combinatorics
2011/9/15
Abstract: We show that if G is a group of automorphisms of a thick finite generalised quadrangle Q acting primitively on both the points and lines of Q, then G is almost simple. Moreover, if G is also...
On a Generalization of Bernoulli and Euler Numbers
Generalization of Bernoulli Euler Numbers Combinatorics
2011/9/15
Abstract: We introduce a series of numbers which serve as a generalization of Bernoulli, Euler numbers and binomial coefficients. Their properties are applied to solve a probability problem and sugges...
On the enumeration of three-rowed standard Young tableaux of skew shape in terms of Motzkin numbers
three-rowed standard Young tableaux Combinatorics
2011/9/15
Abstract: The enumeration of standard Young tableaux (SYTs) of shape {\lambda} can be easily computed by the hook-length formula. In 1981, Amitai Regev proved that the number of SYTs having at most th...
Redundant generating functions in lattice path enumeration
lattice path enumeration Combinatorics Redundant generating functions
2011/9/15
Abstract: A redundant generating function is a generating function having terms which are not part of the solution of the original problem. We use redundant generating functions to study two path prob...
On the metric dimension of line graphs
Metric dimension resolving set line graph de Brujin digraph Kautz digraph
2011/9/16
Abstract: Let $G$ be a (di)graph. A set $W$ of vertices in $G$ is a \emph{resolving set} of $G$ if every vertex $u$ of $G$ is uniquely determined by its vector of distances to all the vertices in $W$....
Crystal rules for $(\ell,0)$-JM partitions
Crystal rules Combinatorics Representation Theory
2011/9/14
Abstract: Vazirani and the author \cite{BV} gave a new interpretation of what we called $\ell$-partitions, also known as $(\ell,0)$-Carter partitions. The primary interpretation of such a partition $\...
Expansion of $k$-Schur functions for maximal $k$-rectangles within the affine nilCoxeter algebra
$k$-Schur functions $k$-rectangles affine nilCoxeter algebra Combinatorics
2011/9/14
Abstract: We give several explicit combinatorial formulas for the expansion of $k$-Schur functions indexed by maximal $k$-rectangles, $s_R^{(k)}$, in terms of the standard basis of the affine nilCoxet...
Sums of Ceiling Functions Solve Nested Recursions
Nested recursion Ceiling function Formal satisfaction Equivalence class
2011/9/15
Abstract: It is known that, for given integers s \geq 0 and j > 0, the nested recursion R(n) = R(n - s - R(n - j)) + R(n - 2j - s - R(n - 3j)) has a closed form solution for which a combinatorial inte...
Abstract: In this paper we define homological stabilizer codes which encompass codes such as Kitaev's toric code and the topological color codes. These codes are defined solely by the graphs they resi...
Krausz dimension and its generalizations in special graph classes
Krausz dimension intersection graphs linear k-uniform hypergraphs chordal graphs polar graphs
2011/9/14
Abstract: A {\it krausz $(k,m)$-partition} of a graph $G$ is the partition of $G$ into cliques, such that any vertex belongs to at most $k$ cliques and any two cliques have at most $m$ vertices in com...
A multivariate "inv" hook formula for forests
hook formula forests moulds binary search free quasisymmetric functions Loday-Ronco algebra
2011/9/14
Abstract: Bjoerner and Wachs provided two q-generalizations of Knuth's hook formula counting linear extensions of forests: one involving the major index statistic, and one involving the inversion numb...
Abstract: Using ultrafilter techniques we show that in any partition of $\mathbb{N}$ into 2 cells there is one cell containing infinitely many exponential triples, i.e. triples of the kind $a,b,a^b$ (...
Scott's induced subdivision conjecture for maximal triangle-free graphs
Scott's subdivision conjecture maximal triangle-free graphs Combinatorics
2011/9/14
Abstract: Scott conjectured that the class of graphs with no induced subdivision of a given graph is $\chi$-bounded. We verify his conjecture for maximal triangle-free graphs.
Abstract: While it is trivial to multiply two C-finite sequences (just like integers), it is not quite so trivial to "factorize" them, or to decide whether they are "prime". The former is plain linear...
Intervals of balanced binary trees in the Tamari lattice
balanced binary tree Tamari lattice poset grammar generating series fixed-point functional equation
2011/9/14
Abstract: We show that the set of balanced binary trees is closed by interval in the Tamari lattice. We establish that the intervals [T, T'] where T and T' are balanced binary trees are isomorphic as ...