16 citations · 21 across the 9 of their papers we have counts for
10 papers
Standard Young tableaux and lattice paths
Shaun V. Ault
Using lattice path counting arguments, we reproduce a well known formula for the number of standard Young tableaux. We also produce an interesting new formula for tableaux of heigh…
Counting paths in corridors using circular Pascal arrays
Shaun V. Ault, Charles Kicey
A circular Pascal array is a periodization of the familiar Pascal's triangle. Using simple operators defined on periodic sequences, we find a direct relationship between the ranges…
Bott periodicity in the Hit Problem
Shaun V. Ault
In this short note, we use Robert Bruner's -resolution of to shed light on the Hit Problem. In particular, the reduced syzygies of o…
Erdos-Szekeres tableaux
Shaun V. Ault, Benjamin Shemmer
We explore a question related to the celebrated Erdős-Szekeres Theorem and develop a geometric approach to answer it. Our main object of study is the Erdős-Szekeres tableau, or EST…
Relations among the kernels and images of {S}teenrod squares acting on right -modules
Shaun V. Ault
In this note, we examine the right action of the Steenrod algebra on the homology groups $H_*(BV_s, \F_2)$, where $V_s = \F_2^s$. We find a relationship between the i…
On the Homology of Elementary Abelian Groups as Modules over the Steenrod Algebra
Shaun V. Ault, William Singer
We examine the dual of the so-called "hit problem", the latter being the problem of determining a minimal generating set for the cohomology of products of infinite projective space…
Homology Operations in Symmetric Homology
Shaun V. Ault
The symmetric homology of a unital associative algebra over a commutative ground ring , denoted , is defined using derived functors and the symmetric bar constructi…
Symmetric Homology of Algebras
Shaun V. Ault
The symmetric homology of a unital algebra over a commutative ground ring is defined using derived functors and the symmetric bar construction of Fiedorowicz. For a group r…
On the Symmetric Homology of Algebras
Shaun Ault
Symmetric homology is an analog of cyclic homology in which the cyclic groups are replaced by symmetric groups. The foundations for the theory of symmetric homology of algebras are…
Symmetric Homology of Algebras
Shaun Ault, Zbigniew Fiedorowicz
In this note, we outline the general development of a theory of symmetric homology of algebras, an analog of cyclic homology where the cyclic groups are replaced by symmetric group…