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On the linear k-arboricity of Kn and Kn,n

2002
*
Discrete Mathematics
*

*The*

*linear*

*k*-

*arboricity*

*of*G, denoted by la

*k*(G), is

*the*minimum number

*of*

*linear*

*k*-forests needed to partition

*the*edge set E(G)

*of*G. ... In this paper, we ÿrst prove that a conjecture by Habib

*and*Peroche holds when G is

*Kn*or

*Kn*;

*n*

*and*

*k*is not less than half

*the*order. ... Acknowledgements

*The*authors do appreciate

*the*referee for

*the*detailed suggestions

*and*corrections to make

*the*paper fruitful,

*and*wish to thank Prof. Hung-Lin Fu for his valuable help. ...

##
###
A Generalization of Linear Indexed Grammars Equivalent to Simple Context-Free Tree Grammars
[chapter]

2014
*
Lecture Notes in Computer Science
*

I define a generalization

doi:10.1007/978-3-662-44121-3_6
fatcat:6cl6a7dscnhnjktffgsibmwn5i
*of**linear*indexed grammars that is equivalent to simple context-free tree grammars in*the*same way that*linear*indexed grammars are equivalent to tree-adjoining grammars. ... C*n*[] is a (DIST) production in P*and*0 ≤*k*1 ≤ · · · ≤*k**n*=*k*, then P contains*the*production . . . , x k1 ) , . . . , C*n*B*kn*−1+1 . . . B*kn*(x*kn*−1+1 , . . . , x*kn*)). ... . , x*k*] = A(u[D 1 (t 1 [x 1 , . . . , x k1 ]), . . . , D*n*(t*n*[x*kn*−1+1 , . . . , x*kn*])]). Then τ = t[B 1 , . . . , B*k*]*and*we have AB 1 . . . ...##
###
Page 8275 of Mathematical Reviews Vol. , Issue 2003k
[page]

2003
*
Mathematical Reviews
*

F(—

*n*,1;*kn*+/+1;2)*and*F((*k*+1)*n*+/1+1,*kn*+1;*kn*+1,*kn*+1+1;z) have identical zero- sets which cluster*on**the*outer loop*of*(*k*+ 1)**!|z|*k*=*k**|z — I|*K*+! ... For k>0*and*/ > 0,*the*zeros*of*F(—*n*,*kn*+ 1+1;*kn*+1+2;z) cluster*on**the*loop*of*|z*(z —1)| = q’yn with Re(z) > 745 l—ka, F(a,1;b+1;2z)*and*F(b—a+1,6;b+1;2) have no zeros in |z— LEE | < ! ...##
###
Page 2455 of Mathematical Reviews Vol. , Issue 98D
[page]

1998
*
Mathematical Reviews
*

A probability measure u

*on*R¢ is said to belong to*the*generalized domain*of*semistable attraction*of*a probability measure vy if there are*linear*operators A,, vectors a,,*and*a sequence*of*integers*k*... Under*the*assumptions that liMy oo*Kn*= 00, O< py, <1*and*lim, K_(1 — pz) = A € [0, 00), we investigate limit distributions*of*{7,,(*k*,)}.” 984:60052 60F05S Sholomitskii, A. G. ...##
###
Dendritic Cytoskeletal Architecture Is Modulated by Combinatorial Transcriptional Regulation in Drosophila melanogaster

2017
*
Genetics
*

*arbor*morphology, respectively. ... These analyses identified a host

*of*putative Cut

*and*/or Knot effector molecules,

*and*a subset

*of*these putative TF targets converge

*on*modulating dendritic cytoskeletal architecture, which are grouped ... Doe (University

*of*Oregon/HHMI),

*and*Y.-

*N*. Jan for sharing

*the*transgenic strains. We thank D. A. ...

##
###
The linear (n-1)-arboricity of Cartesian product graphs

2015
*
Applicable Analysis and Discrete Mathematics
*

In this paper,

doi:10.2298/aadm150202003z
fatcat:r5ntwvgaijcqznx6hpkbcbtkvu
*the*exact values*of**the**linear*(*n*− 1)-*arboricity**of*Hamming graph,*and*Cartesian product graphs C m nt*and**Kn**Kn*,*n*are obtained. 2010 Mathematics Subject Classification: 05C15. ...*The**linear**k*-*arboricity**of*G, denoted by la*k*(G), is*the*minimum number*of**linear**k*-forests needed to partition*the*edge set E(G)*of*G. ...*The**linear*2-*arboricity*,*the**linear*3-*arboricity**and**the*low bound*of**linear**k*-*arboricity**of*balanced complete bipartite graphs are obtained in [9, 10, 11] , respectively. ...##
###
Page 2188 of Mathematical Reviews Vol. , Issue 94d
[page]

1994
*
Mathematical Reviews
*

Setting u, =

*n*ome Q(u) du*and*o, = /na(*k*,/*n*), where o2(s) = “ty » *[min(u, v) —uv]dQ(u)dQ(v), 0<s <1, we know that*the*asymptotic distribution*of*Z,(*k*,) = [Sn(*kn*) — Un]/*on*is stan- dard normal. ... For*k*=*k*(*n*) define*the**k*- discrepancy Dk (X 1,°-',Xw) to be*the*maximum*of*1*ONS*REN IE: Man SO EIS. tas Vv PF ux(A)*N*over all A € {0,1}*, where 4, denotes*the**k*-fold product*of**the*above probability ...##
###
Page 6 of Mathematical Reviews Vol. 25, Issue 1
[page]

1963
*
Mathematical Reviews
*

In this note, it is shown that

*the*number*of*labeled bicolored trees with m points*of**one*color*and**n*points*of**the*other is n™~1m*~!. ... This general- izes*the*well-known result*of*Cayley that*the*number*of*labeled trees with*n*points is n™~?. F. Harary (Ann*Arbor*, Mich.) Ore, Oystein 25 Incidence matchings in graphs. J. Math. ...##
###
Page 843 of Mathematical Reviews Vol. 26, Issue 4
[page]

1963
*
Mathematical Reviews
*

Further, let {a,,;

*n*=1, 2, :*k*=1, 2, be a ‘double sequence*of*real constants,*and*let {len} be a sequence*of*— ye*on*such that Guz, #0*and*Gnx=0 for*k*>*kn*,*n*=1, 2, . ... ,*One*® = Var Enk,*k*=1*and*put*kn*(2) ln as B," 2, OnkEnk,*n*= L, 2, —*The*author investigates necessary*and*sufficient condi- tions*on**the*set F*and**on**the*double sequence {a,x} in order that*the*d.f.’s ...##
###
An equivariant isomorphism theorem for mod p reductions of arboreal Galois representations
[article]

2020
*
arXiv
*
pre-print

As an application

arXiv:1905.00506v3
fatcat:uct7yq6rovd7bfu2ofkflj4kjm
*of*our results we prove R. Jones' conjecture*on**the**arboreal*Galois representation attached to*the*polynomial x^2+t. ... Using this result, we prove that if ϕ is non-isotrivial*and*geometrically stable then outside a finite, effective set*of*primes*of*O_F,D*the*geometric part*of**the**arboreal*representation*of*ϕ_p is isomorphic ... Recall that inequality (11) now reads: h*Kn*(c*n*−2 ) ≤ 8p e (h(d*n*) + 2g*K*+ |W |) + h*Kn*(α 1 + α 3 ) + h*Kn*(α 2 − α 1 ), where g*K*is*the*genus*of**K**and*W is*the*set*of*valuations w*of**K**n*such that ...##
###
Linear k-arboricities on trees

2000
*
Discrete Applied Mathematics
*

For a ÿxed positive integer

doi:10.1016/s0166-218x(99)00247-4
fatcat:k5elo3xyjzekranfqnsgs5rgqi
*k*,*the**linear**k*-*arboricity*la*k*(G)*of*a graph G is*the*minimum number ' such that*the*edge set E(G) can be partitioned into ' disjoint sets*and*that each induces a subgraph ... This paper studies*linear**k*-*arboricity*from an algorithmic point*of*view. In particular, we present a*linear*-time algorithm to determine whether a tree T has la*k*(T )6m. ? ... Acknowledgements*The*authors thank*the*referee for many constructive suggestions. In particular,*the*suggestions*on*Algorithm L make it clear that*the*algorithm is*linear*. ...##
###
Page 207 of Mathematical Reviews Vol. 18, Issue 3
[page]

1957
*
Mathematical Reviews
*

In particular, it is shown that
Px

*n*(2)=Axk,n2™'1F 1(—nx, (2ng*+-1)/*k*; 2*), where*n*=*n*,zk-+*n*,*, Osm*<*k*,*and*A,» is known*and*that*the*system {Pz} is involutive, possessing 2* involutive forms.*N*. D. ... By general theorems, (A) is equivalent to (C): every*linear*functional*on*X, ing*on*S, vanishes identically.*The*author first shows that (B)*and*© are equivalent in general; hence so are (A)*and*(B). ...##
###
ALGORITHMIC ASPECTS OF LINEAR k-ARBORICITY

1999
*
Taiwanese journal of mathematics
*

For a fixed positive integer

doi:10.11650/twjm/1500407055
fatcat:tx7fjuyusjcevccd4u46qrg2hi
*k*,*the**linear**k*-*arboricity*la*k*(G)*of*a graph G is*the*minimum number such that*the*edge set E(G) can be partitioned into disjoint sets, each induces a subgraph whose components ... This paper examines*linear**k*-*arboricity*from an algorithmic point*of*view. In particular, we present a*linear*-time algorithm for determining whether a tree T has la 2 (T ) ≤ m. ... Acknowledgements*The*author thanks Kuo-Ching Huang for pointing out a serious mistake in a previous version*of**the*paper. ...##
###
Page 331 of Mathematical Reviews Vol. 11, Issue 5
[page]

1950
*
Mathematical Reviews
*

Tornheim (Ann

*Arbor*, Mich.). Erdés, P.,*and*Koksma, J. F.*On**the*uniform distri- bution modulo 1*of*sequences (f(,@)). Nederl. Akad. ... Then for «>0*and*almost all @*the*discrepancy D(*N*, @)*of**the*sequence f(1, 6), f(2, 0), f(3, 0), «+> satisfies*the*inequality ND(*N*, @) =O(*N*# log®™*+**N*).*K*. Mahler (Manchester). Erdés, P. ...##
###
Page 1458 of Mathematical Reviews Vol. 22, Issue 9B
[page]

1961
*
Mathematical Reviews
*

*The*main result

*of*

*the*paper is

*the*following: Let p,(z)= > Parz* ; then 7a Pat = * +0(1) (Osksn< ow), where 0(1)—>0 as

*n*—

*k*->oo uniformly in

*k*

*and*

*n*. U. Grenander (Stockholm) 8548 : Sarmanov, 0. ... Wendel (Ann

*Arbor*, Mich.) 1458 PROBABILITY 8549: Bahadur, R. R.; Ranga Rao, R.

*On*deviations

*of*

*the*sample mean. Ann. Math. Statist. 31 (1960), 1015-1027. ...

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