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

Bor-Liang Chen, Kuo-Ching Huang
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]

Makoto Kanazawa
2014 Lecture Notes in Computer Science
I define a generalization 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

Ravi Das, Shatabdi Bhattacharjee, Atit A. Patel, Jenna M. Harris, Surajit Bhattacharya, Jamin M. Letcher, Sarah G. Clark, Sumit Nanda, Eswar Prasad R. Iyer, Giorgio A. Ascoli, Daniel N. Cox
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

Liancui Zuo, Shengjie He, Bing Xue
2015 Applicable Analysis and Discrete Mathematics
In this paper, 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]

Andrea Ferraguti, Giacomo Micheli
2020 arXiv   pre-print
As an application 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

Gerard J. Chang, Bor-Liang Chen, Hung-Lin Fu, Kuo-Ching Huang
2000 Discrete Applied Mathematics
For a ÿxed positive integer 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

Gerard J. Chang
1999 Taiwanese journal of mathematics
For a fixed positive integer 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 nk->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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