Self-Dual Interval Orders and Row-Fishburn Matrices

نویسندگان

Sherry H. F. Yan

Yuexiao Xu

چکیده

Recently, Jeĺınek derived that the number of self-dual interval orders of reduced size n is twice the number of row-Fishburn matrices of size n by using generating functions. In this paper, we present a bijective proof of this relation by establishing a bijection between two variations of upper-triangular matrices of nonnegative integers. Using the bijection, we provide a combinatorial proof of the refined relations between self-dual Fishburn matrices and row-Fishburn matrices in answer to a problem proposed by Jeĺınek.

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

Asymptotics for the number of row-Fishburn matrices

In this paper, we provide an asymptotic for the number of row-Fishburn matrices of size n which settles a conjecture by Vit Jeĺınek. Additionally, using q-series constructions we provide new identities for the generating functions for the number of such matrices, one of which was conjectured by Peter Bala.

متن کامل

Hadamard matrices of order 36 and double-even self-dual [72,36,12] codes

A balanced incomplete block design (BIBD) [1] with parameters 2-(v, b, r, k, λ) (short 2-(v, k, λ)) is a pair (V,B) where V is a v-set (elements are called points) and B is a collection of b k-subsets (elements are called blocks) of V such that each point is contained in exactly r blocks and any pair of points is contained in exactly λ blocks. A Hadamard matrix of order n is an n × n (1,−1)-mat...

متن کامل

Matrices of Varied Orthogonality and Their Codes (Submitted for short presentation at ISIT'98.)

Orthogonal matrices over arbitrary elds are de ned together with their non-square analogs, which are termed row-orthogonal matrices. Antiorthogonal and self-orthogonal square matrices are introduced together with their non-square analogs. The relationships of these matrices to such codes as self-dual codes and linear codes with complementary duals are given.

متن کامل

Interval Orders and Reverse Mathematics

We study the reverse mathematics of interval orders. We establish the logical strength of the implications between various definitions of the notion of interval order. We also consider the strength of different versions of the characterization theorem for interval orders: a partial order is an interval order if and only if it does not contain 2 ⊕ 2. We also study proper interval orders and thei...

متن کامل