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COMBINATORICS
1998
61views more  COMBINATORICS 1998»
11 years 6 months ago
A Macdonald Vertex Operator and Standard Tableaux Statistics
On donnera une formule pour l’op´erateur Hqt 2 avec la propri´et´e que Hqt 2 H(2a1b)[X; q, t] = H(2a+11b)[X; q, t] avec les fonctions sym´etriques Hµ[X; q, t] = λ Kλµ(q,...
Mike Zabrocki
COMBINATORICS
1998
99views more  COMBINATORICS 1998»
11 years 6 months ago
On Minimal Words With Given Subword Complexity
We prove that the minimal length of a word Sn having the property that it contains exactly Fm+2 distinct subwords of length m for 1 ≤ m ≤ n is Fn + Fn+2. Here Fn is the nth Fi...
Ming-wei Wang, Jeffrey Shallit
COMBINATORICS
1998
88views more  COMBINATORICS 1998»
11 years 6 months ago
A Bijective Proof of Garsia's q-Lagrange Inversion Theorem
A q-Lagrange inversion theorem due to A. M. Garsia is proved by means of two sign-reversing, weight-preserving involutions on Catalan trees.
Dan W. Singer
COMBINATORICS
1998
80views more  COMBINATORICS 1998»
11 years 6 months ago
Increasing Subsequences and the Classical Groups
We show that the moments of the trace of a random unitary matrix have combinatorial interpretations in terms of longest increasing subsequences of permutations. To be precise, we s...
Eric M. Rains
COMBINATORICS
1998
100views more  COMBINATORICS 1998»
11 years 6 months ago
Lattice Paths Between Diagonal Boundaries
A bivariate symmetric backwards recursion is of the form d[m, n] = w0(d[m− 1, n]+d[m, n−1])+ω1(d[m−r1, n−s1]+d[m−s1, n−r1])+· · ·+ωk(d[m−rk, n−sk] +d[m−sk, ...
Heinrich Niederhausen
COMBINATORICS
1998
103views more  COMBINATORICS 1998»
11 years 6 months ago
Recognizing Circulant Graphs of Prime Order in Polynomial Time
A circulant graph G of order n is a Cayley graph over the cyclic group Zn. Equivalently, G is circulant iff its vertices can be ordered such that the corresponding adjacency matr...
Mikhail E. Muzychuk, Gottfried Tinhofer
COMBINATORICS
1998
86views more  COMBINATORICS 1998»
11 years 6 months ago
Lattice Tilings by Cubes: Whole, Notched and Extended
We discuss some problems of lattice tiling via Harmonic Analysis methods. We consider lattice tilings of Rd by the unit cube in relation to the Minkowski Conjecture (now a theorem...
Mihail N. Kolountzakis
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