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A completion of the spectrum for large sets of disjoint transitive triple systems

1992
*
Journal of combinatorial theory. Series A
*

Thereby, we

doi:10.1016/0097-3165(92)90009-j
fatcat:z4p5suncmzasbp7ywzsqpwxeda
*completely*solve*the*existence problem*of*LTTS(V) (*large**set**of*pairwise*disjoint**transitive**triple**systems**of*order 0). ...*A*SYMMETRIC LTTS(24 + 2) In [4, 51 we introduced*a*kind*of*special*large**set**of**disjoint*Mendelsohn*triple**systems*(LMTS)-symmetric LMTS. ...*For*any v-0 or 1 (mod 3), theve exists an LTTS(u). Proof: Let v = 2% + 2, where u = 1 or 5 (mod 6). If n = 0, by (R2), there exists an LTTS(u). ...##
###
Construction of large sets of pairwise disjoint transitive triple systems II

1987
*
Discrete Mathematics
*

*The*maximum number

*of*pairwise

*disjoint*

*transitive*

*triple*

*systems*(T'I'Ss)

*of*order n is 3(n -2). Such

*a*collection is called

*a*

*large*

*set*

*of*pairwise

*disjoint*TI'Ss

*of*order n. ... Two consequences

*of*this result are

*the*existence

*of*

*a*

*large*

*set*

*of*pairwise

*disjoint*TI'Ss

*of*every odd admissible order and

*the*existence

*of*

*a*

*large*

*set*

*of*pairwise

*disjoint*TI'Ss

*of*every admissible ... Construction

*of*

*large*

*sets*

*of*pairwise

*disjoint*

*transitive*

*triple*

*systems*II 73 Corollary 5.2. ...

##
###
Page 4708 of Mathematical Reviews Vol. , Issue 93i
[page]

1993
*
Mathematical Reviews
*

Phelps (Auburn University, AL)
93i:05024 05B07
Kang, Qing De (PRC-HBN); Chang, Yan Xun (PRC-HBN)

*A**completion**of**the**spectrum**for**large**sets**of**disjoint**transitive**triple**systems*. J. Combin. ...*A**transitive**triple**system*(TTS)*of*order n is*a*pair (P,T), where T is*a*collection*of*edge*disjoint**transitive**triples*which partition*the*edge*set**of*D,, with vertex*set*P. ...##
###
Page 5806 of Mathematical Reviews Vol. , Issue 96j
[page]

1996
*
Mathematical Reviews
*

Math. 27 (1975), 256-260; MR 51 #5334] constructed

*for*every n = 1 or 3 (mod 6)*a**large**set**of*n*triple**systems**of*order n which were mutually almost*disjoint*(MAD) ((S, T;) and (S,7;) are almost*disjoint*... It is not hard to see that*a**large**set**of*MAD*triple**systems**of*order n must consist*of*n—1, n, or n+1*triple**systems*. ...##
###
A class of 2-chromatic SQS(22)

1991
*
Discrete Mathematics
*

We enumerate all 2-chromatic Steiner quadruple

doi:10.1016/0012-365x(91)90448-b
fatcat:pjvk6cbgevhmvnkwc6zfmsk2am
*systems**of*order 22, having*a*cyclic automorphism*of*order 11 (i.e. 2*disjoint*ll-cycles). 0012-365X/91/$03.50 0 1991-Elsevier Science Publishers B.V. ... In memory*of*Egmont Kiihler. Abstract Phelps, K.T.,*A*class*of*2khromatic SQS(22), Discrete Mathematics 97 (1991) 333-338. ...*of**triples*is*a*partial*triple**system**of*order II, then this will give us*the*base blocks*for**a**large**set**of*partial*triple**systems*, which we will call*a*cyclic*large**set*. ...##
###
Page 2562 of Mathematical Reviews Vol. , Issue 95e
[page]

1995
*
Mathematical Reviews
*

*spectrum*

*for*

*large*

*sets*

*of*

*disjoint*Mendelsohn

*triple*

*systems*with any index. ... It is well known that

*the*

*spectrum*(=

*set*

*of*all m such that

*a*

*triple*

*system*

*of*order n exists)

*for*

*triple*

*systems*is precisely

*the*

*set*

*of*all »=1 or 3 (mod 6). ...

##
###
Page 4764 of Mathematical Reviews Vol. , Issue 98H
[page]

1998
*
Mathematical Reviews
*

*A*

*large*

*set*

*of*mutually almost

*disjoint*(MAD) Steiner

*triple*

*systems*

*of*order v is

*a*collection

*of*Steiner

*triple*

*systems*on

*the*same v-

*set*S such that every 3-subset

*of*S occurs as

*a*block in at least ... It is well known that

*the*

*spectrum*(=

*set*

*of*all v

*for*which

*a*/-fold directed

*triple*

*system*

*of*order v exists)

*for*3-fold directed

*triple*

*systems*consists

*of*all v > 3. ...

##
###
Page 2266 of Mathematical Reviews Vol. , Issue 85f
[page]

1985
*
Mathematical Reviews
*

It is conjectured that

*a*CSQS(v) exists*for*all admissible orders v except 8, 14 and 16. However,*the**spectrum**for*CSQS(v) has not been*completely*determined. ... An invariant*for*Steiner*triple**systems*(STS) is*a*mapping f defined on*the**set**of*all STSs such that f(D) = f(D’) if D, D’ ...##
###
Page 8081 of Mathematical Reviews Vol. , Issue 2003k
[page]

2003
*
Mathematical Reviews
*

[Zhu, Lie'] (PRC-SOO; Suzhou)
An improved product construction

*for**large**sets**of*Kirkman*triple**systems*. (English summary) Discrete Math. 260 (2003), no. 1-3, 307-313. ... (v) is*a**transitive*Kirkman*triple**system**of*order v, and an LR(uw) is*a*new kind*of*design introduced by Lei. ...##
###
Page 4059 of Mathematical Reviews Vol. , Issue 97G
[page]

1997
*
Mathematical Reviews
*

*A*

*large*

*set*

*of*

*disjoint*resolv- able Mendelson [directed]

*triple*

*systems*

*of*order v, LRMTS(v) {[LRDTS(v)], is

*a*partition

*of*

*the*

*set*

*of*all cyclic [

*transitive*]

*triples*on

*a*v-

*set*into resolvable Mendelsohn ...

*A*directed

*triple*

*system*

*of*or- der v is

*a*decomposition

*of*

*the*

*complete*directed graph, with- out loops, on

*a*v-

*set*into

*transitive*

*triples*, where

*a*

*transitive*

*triple*is defined as an isomorphic copy ...

##
###
Page 1028 of Mathematical Reviews Vol. 48, Issue 4
[page]

1974
*
Mathematical Reviews
*

Two Steiner

*triple**systems*having*the*same*set**of*points are said to be*disjoint*if they have no line in common. ...*The*interest in such*a*stems from*the*fact that*the**triples*{*a*, b, «(b—*a*)+*a*} (*a*,b €S,*a*#b) form*a*Steiner*triple**system**for*which 8 acts as*a*regular,*transitive*automorphism group. ...##
###
Page 2110 of Mathematical Reviews Vol. , Issue 97D
[page]

1997
*
Mathematical Reviews
*

*A*

*large*

*set*

*of*Mendelsohn [directed]

*triple*

*systems*

*of*order v is

*a*collection

*of*v —2

*disjoint*MTS(v) [DTS(v)] whose

*triples*partition

*the*

*set*

*of*all cyclic [directed]

*triples*on

*the*v-

*set*. ...

*A*60 (1992), no. 2, 287-294; MR 93i:05024] that

*large*

*sets*

*of*MTS and DTS exist

*for*all v = 0,1 (mod 6) except

*for*v = 6 in

*the*case

*of*

*a*

*large*

*set*

*of*MTS. ...

##
###
Page 3199 of Mathematical Reviews Vol. , Issue 2003e
[page]

2003
*
Mathematical Reviews
*

*A*

*large*

*set*

*of*

*disjoint*Kirkman

*triple*

*systems*

*of*order v, or LKTS(wv), isa partition

*of*

*the*

*set*

*of*all 3-subsets

*of*

*a*v-

*set*into v — 2 Kirkman

*triple*

*systems*

*of*order v. ...

*For*u = 1,

*the*existence

*of*

*a*KS; (v; “4, 4) is equivalent to

*the*existence

*of*

*a*doubly resolvable (v,k,2)-BIBD.

*The*

*spectrum*

*of*KS;(v;1,1) or Room squares was

*completed*by Mullin and Wallis in 1975. ...

##
###
Topological Effects in Tunneling-Coupled Systems of One-Dimensional Quantum Rings
[article]

2020
*
arXiv
*
pre-print

We find that writhe not only determines

arXiv:2007.01967v1
fatcat:avvfbij2crbtrcty2hlnsyacre
*the*energetic response*of**the**system*to magnetic field strength, but is also responsible*for**a*single particle topological quantum phase*transition*involving*the*... Using*a*model*of*idealized, crossed one-dimensional quantum wires we construct*a*novel model*for**a*single electron on tunneling-coupled*systems**of*one-dimensional quantum rings. ... (*a*) is*the**spectrum**for**the*two ring*system*, and (b) is*the**spectrum**for**the*figure eight*system*. ...##
###
Large sets of oriented triple systems with resolvability

2000
*
Discrete Mathematics
*

In this paper, we summarize

doi:10.1016/s0012-365x(99)00288-5
fatcat:uurr5dhszzanjlvmhtme2xd3wm
*the*present situation about*large**sets*(resp. overlarge*sets*)*of*several types*of**triple**systems*and give some new results. ... is*a*partition*of*X (or X \{x}*for*some x ∈ X ). ...*The**system*is denoted by TKTS(v) = (X; B; G).*The*design TKTS(v) has played an important role to construct*large**sets**of**disjoint*Kirkman*triple**systems*. ...
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