One-dimensional optimal bounded-shape partitions for Schur convex sum objective functions

نویسندگان

  • F. H. Chang
  • H. B. Chen
  • J. Y. Guo
  • Frank K. Hwang
  • Uriel G. Rothblum
چکیده

Consider the problem of partitioning n nonnegative numbers into p parts, where part i can be assigned ni numbers with ni lying in a given range. The goal is to maximize a Schur convex function F whose i th argument is the sum of numbers assigned to part i . The shape of a partition is the vector consisting of the sizes of its parts, further, a shape (without referring to a particular partition) is a vector of nonnegative integers (n1, . . . , n p) which sum to n. A partition is called size-consecutive if there is a ranking of the parts which is consistent with their sizes, and all elements in a higher-ranked part exceed all elements in the lower-ranked part. We demonstrate that one can restrict attention to size-consecutive partitions with shapes that are nonmajorized, we study these shapes, bound their numbers and develop algorithms to enumerate them. Our study extends the analysis of a previous paper by Hwang and Rothblum which discussed the above problem assuming the existence of a majorizing shape.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

The role of residue and quotient tables in the theory of k-Schur functions

Recently, residue and quotient tables were defined by Fishel and the author, and were used to describe strong covers in the lattice of k-bounded partitions. In this paper, we show or conjecture that residue and quotient tables can be used to describe many other results in the theory of k-bounded partitions and k-Schur functions, including k-conjugates, weak horizontal and vertical strips, and t...

متن کامل

Total Capacity of Multiaccess Vector Channels

The well known waterrlling power allocation policy maximizes the sum capacity of parallel Gaussian channels. We consider multiaccess vector channels with additive colored Gaussian noise and asymmetric user power constraints and completely characterize the sum capacity of this channel. We show that the sum capacity of the multiaccess vector channel is upper bounded by that of corresponding paral...

متن کامل

Functionally closed sets and functionally convex sets in real Banach spaces

‎Let $X$ be a real normed  space, then  $C(subseteq X)$  is  functionally  convex  (briefly, $F$-convex), if  $T(C)subseteq Bbb R $ is  convex for all bounded linear transformations $Tin B(X,R)$; and $K(subseteq X)$  is  functionally   closed (briefly, $F$-closed), if  $T(K)subseteq Bbb R $ is  closed  for all bounded linear transformations $Tin B(X,R)$. We improve the    Krein-Milman theorem  ...

متن کامل

A Factorization Theorem for Classical Group Characters, with Applications to Plane Partitions and Rhombus Tilings

1 , . . . , xn, x −1 n factorizes into a product of two odd orthogonal characters of rectangular shape, one of which is evaluated at −x1, . . . ,−xn, if M is even, while it factorizes into a product of a symplectic character and an even orthogonal character, both of rectangular shape, if M is odd. It is furthermore shown that the first factorization implies a factorization theorem for rhombus t...

متن کامل

Plane Partitions

Throughout our study of the enumeration of plane partitions we make use of bijective proofs to find generating functions. In particular, we consider bounded plane partitions, symmetric plane partitions and weak reverse plane partitions. Using the combinatorial interpretations of Schur functions in relation to semistandard Young tableaux, we rely on the properties of symmetric functions. In our ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • J. Comb. Optim.

دوره 11  شماره 

صفحات  -

تاریخ انتشار 2006