Primitive symmetric designs with prime power number of points

2009 ◽  
pp. n/a-n/a
Author(s):  
Snježana Braić ◽  
Anka Golemac ◽  
Joško Mandić ◽  
Tanja Vučičić
Keyword(s):  
Prime Power ◽  
Power Number ◽  
Symmetric Designs

A Polynomial Model for Logics with a Prime Power Number of Truth Values

2010 ◽  
Vol 46 (2) ◽  
pp. 205-221 ◽  
Author(s):  
Antonio Hernando ◽  
Eugenio Roanes-Lozano ◽  
Luis M. Laita
Keyword(s):  
Prime Power ◽  
Polynomial Model ◽  
Power Number ◽  
Truth Values

scholarly journals Applying Balanced Generalized Weighing Matrices to Construct Block Designs

10.37236/1556 ◽  
2001 ◽  
Vol 8 (1) ◽  
Author(s):  
Yury J. Ionin
Keyword(s):  
Positive Integer ◽  
Prime Power ◽  
Block Designs ◽  
Weighing Matrices ◽  
Symmetric Designs

Balanced generalized weighing matrices are applied for constructing a family of symmetric designs with parameters $(1+qr(r^{m+1}-1)/(r-1),r^{m},r^{m-1}(r-1)/q)$, where $m$ is any positive integer and $q$ and $r=(q^{d}-1)/(q-1)$ are prime powers, and a family of non-embeddable quasi-residual $2-((r+1)(r^{m+1}-1)/(r-1),r^{m}(r+1)/2,r^{m}(r-1)/2)$ designs, where $m$ is any positive integer and $r=2^{d}-1$, $3\cdot 2^{d}-1$ or $5\cdot 2^{d}-1$ is a prime power, $r\geq 11$.

scholarly journals On the Twin Designs with the Ionin–type Parameters

10.37236/1479 ◽  
1999 ◽  
Vol 7 (1) ◽  
Author(s):  
H. Kharaghani
Keyword(s):  
Positive Integer ◽  
Prime Power ◽  
Hadamard Matrix ◽  
Hadamard Matrices ◽  
Symmetric Designs ◽  
New Class

Let $4n^2$ be the order of a Bush-type Hadamard matrix with $q=(2n-1)^2$ a prime power. It is shown that there is a weighing matrix $$ W(4(q^m+q^{m-1}+\cdots+q+1)n^2,4q^mn^2) $$ which includes two symmetric designs with the Ionin–type parameters $$ \nu=4(q^m+q^{m-1}+\cdots+q+1)n^2,\;\;\; \kappa=q^m(2n^2-n), \;\;\; \lambda=q^m(n^2-n) $$ for every positive integer $m$. Noting that Bush–type Hadamard matrices of order $16n^2$ exist for all $n$ for which an Hadamard matrix of order $4n$ exist, this provides a new class of symmetric designs.

scholarly journals A Generalization of Partition Identities for First Differences of Partitions of $n$ Into at Most $m$ Parts

10.37236/8199 ◽  
2021 ◽  
Vol 28 (3) ◽  
Author(s):  
Acadia Larsen
Keyword(s):  
Finite Number ◽  
Linear Combination ◽  
Prime Power ◽  
Power Number ◽  
Partition Identities ◽  
Partition Identity ◽  
Combinatorial Interpretations ◽  
Finite Set

We show for a prime power number of parts $m$ that the first differences of partitions into at most $m$ parts can be expressed as a non-negative linear combination of partitions into at most $m-1$ parts. To show this relationship, we combine a quasipolynomial construction of $p(n,m)$ with a new partition identity for a finite number of parts. We prove these results by providing combinatorial interpretations of the quasipolynomial of $p(n,m)$ and the new partition identity.  We extend these results by establishing conditions for when partitions of $n$ with parts coming from a finite set $A$ can be expressed as a non-negative linear combination of partitions with parts coming from a finite set $B$.

scholarly journals New symmetric designs from regular Hadamard matrices

10.37236/1339 ◽  
1997 ◽  
Vol 5 (1) ◽  
Author(s):  
Yury J. Ionin
Keyword(s):  
Positive Integer ◽  
Prime Power ◽  
Hadamard Matrices ◽  
Weighing Matrices ◽  
Symmetric Designs ◽  
Parameter Values

For every positive integer $m$, we construct a symmetric $(v,k,\lambda )$-design with parameters $v={{h((2h-1)^{2m}-1)}\over{h-1}}$, $k=h(2h-1)^{2m-1}$, and $\lambda =h(h-1)(2h-1)^{2m-2}$, where $h=\pm 3\cdot 2^d$ and $|2h-1|$ is a prime power. For $m\geq 2$ and $d\geq 1$, these parameter values were previously undecided. The tools used in the construction are balanced generalized weighing matrices and regular Hadamard matrices of order $9\cdot 4^d$.

scholarly journals Groups with a Cayley graph isomorphic to a hypercube

1997 ◽  
Vol 55 (3) ◽  
pp. 385-393
Author(s):  
John D. Dixon
Keyword(s):  
Cayley Graph ◽  
Prime Power ◽  
Cayley Graphs ◽  
Power Number

A process is described for enumerating the Cayley graphs isomorphic to a binary d-cube for small values of d. There are 4 Cayley graphs isomorphic to the 3-cube, 14 isomorphic to the 4-cube, 45 isomorphic to the 5-cube and 238 isomorphic to the 6-cube. A similar method may be used for any graph with a prime power number of vertices.

Surface Aeration Threshold in Agitated Vessels

1996 ◽  
Vol 61 (5) ◽  
pp. 681-690
Author(s):  
Kamil Wichterle ◽  
Tomáš Svěrák
Keyword(s):  
Simple Model ◽  
Liquid Surface ◽  
Power Input ◽  
Power Number ◽  
Region Analysis ◽  
Surface Aeration ◽  
Liquid Dispersion ◽  
Mixing Vessels ◽  
Number Curve

Violent agitation of liquids in mixing vessels may result in the regime of surface aeration being attained when the bubbles formed at the liquid surface enter the impeller region. Analysis of data on surface aeration for different liquids in a set of geometrically similar agitated vessels is presented. Data on the just aerated state as observed visually in transparent liquids, and data for the efficient aeration as determined from the break on the power number curve are considered. A simple model is developed for correlation of the data which enables the threshold of aeration to be predicted from the value of the recirculation number Nc = Nd (ρ/σg)1/4. The possibility of interpreting various literature data for the aeration threshold and for the power input with use of Nc is demonstrated. Similar modelling rules hold also for the correlation of beginning of the efficient liquid-liquid dispersion.

scholarly journals An infinite family of Williamson matrices

1977 ◽  
Vol 24 (2) ◽  
pp. 252-256 ◽  
Author(s):  
Edward Spence
Keyword(s):  
Prime Power ◽  
Hadamard Matrix ◽  
Infinite Family ◽  
Williamson Matrices

AbstractIn this paper the following result is proved. Suppose there exists a C-matrix of order n + 1. Then if n≡1 (mod 4) there exists a Hadamard matrix of order 2nr(n + 1), while if n≡3 (mod 4) there exists a Hadamard matrix of order nr(n + 1) for all r ≧0. If n≡1 (mod 4) is a prime power, the method is adapted to prove the existence of a Hadamard matrix of the Williamson type, of order 2nr(n + 1), for all r ≧0.

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