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pro vyhledávání: '"Ault, Shaun V."'
Autor:
Ault, Shaun V.
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 height $\leq 3$ using the Fourier methods of Ault and Kicey.
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Externí odkaz:
http://arxiv.org/abs/2201.02540
Autor:
Ault, Shaun V.
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 developed in the context of crossed simplicial groups using derived f
Externí odkaz:
http://rave.ohiolink.edu/etdc/view?acc_num=osu1218237992
Autor:
Ault, Shaun V., Kicey, Charles
Publikováno v:
Shaun V. Ault and Charles Kicey. Counting paths in corridors using circular Pascal arrays. Discrete Mathematics 332(6):45-54, October 2014
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 of the circular Pascal arrays and numbers of certain lattice paths wi
Externí odkaz:
http://arxiv.org/abs/1407.2197
Autor:
Ault, Shaun V., Shemmer, Benjamin
Publikováno v:
S. V. Ault and B. Shemmer. Erdos-Szekeres tableaux. Order, pages 1-12, 2013
We explore a question related to the celebrated Erd\H{o}s-Szekeres Theorem and develop a geometric approach to answer it. Our main object of study is the Erd\H{o}s-Szekeres tableau, or EST, of a number sequence. An EST is the sequence of integral poi
Externí odkaz:
http://arxiv.org/abs/1407.0579
Autor:
Ault, Shaun V.
Publikováno v:
Mathematical Proceedings of the Cambridge Philosophical Society, 156:545-554, 3 2014
In this short note, we use Robert Bruner's $\mathcal{A}(1)$-resolution of $P = \mathbb{F}_2[t]$ to shed light on the Hit Problem. In particular, the reduced syzygies $P_n$ of $P$ occur as direct summands of $\widetilde{P}^{\otimes n}$, where $\wideti
Externí odkaz:
http://arxiv.org/abs/1406.7734
Autor:
Ault, Shaun V.
Publikováno v:
Shaun V. Ault. Relations among the kernels and images of Steenrod squares acting on right A-modules. Journal of Pure and Applied Algebra 216 (2012), 1428-1437
In this note, we examine the right action of the Steenrod algebra $\mathcal{A}$ on the homology groups $H_*(BV_s, \F_2)$, where $V_s = \F_2^s$. We find a relationship between the intersection of kernels of $Sq^{2^i}$ and the intersection of images of
Externí odkaz:
http://arxiv.org/abs/1106.3012
Autor:
Ault, Shaun V., Singer, William
Publikováno v:
Shaun V. Ault and William Singer. On the homology of elementary Abelian groups as modules over the Steenrod algebra. Journal of Pure and Applied Algebra 215 (2011), 2847-2852
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 spaces as module over the Steenrod Algebra $\mathcal{A}$ at the prime 2. Th
Externí odkaz:
http://arxiv.org/abs/1105.1139
Publikováno v:
Gregory V. Bard, Shaun V. Ault, and Nicholas T. Courtois. Statistics of random permutations and the cryptanalysis of periodic block ciphers. Cryptologia 36 (2012) 240-262
A block cipher is intended to be computationally indistinguishable from a random permutation of appropriate domain and range. But what are the properties of a random permutation? By the aid of exponential and ordinary generating functions, we derive
Externí odkaz:
http://arxiv.org/abs/0905.3682
Autor:
Ault, Shaun V.
The symmetric homology of a unital associative algebra $A$ over a commutative ground ring $k$, denoted $HS_*(A)$, is defined using derived functors and the symmetric bar construction of Fiedorowicz. In this paper we show that $HS_*(A)$ admits homolog
Externí odkaz:
http://arxiv.org/abs/0904.1023
Autor:
Ault, Shaun V.
Publikováno v:
Ault, S. V. Symmetric Homology of Algebras, Algebraic & Geometric Topology 10 (2010) 2343-2408
The symmetric homology of a unital algebra $A$ over a commutative ground ring $k$ is defined using derived functors and the symmetric bar construction of Fiedorowicz. For a group ring $A = k[\Gamma]$, the symmetric homology is related to stable homot
Externí odkaz:
http://arxiv.org/abs/0902.1274