scholarly journals Graph universal cycles of combinatorial objects

2021 ◽  
Vol 127 ◽  
pp. 102166
Author(s):  
Amelia Cantwell ◽  
Juliann Geraci ◽  
Anant Godbole ◽  
Cristobal Padilla
Keyword(s):  
Combinatorial Objects ◽  
Universal Cycles

scholarly journals On Universal Cycles of Labeled Graphs

10.37236/276 ◽  
2010 ◽  
Vol 17 (1) ◽  
Author(s):  
Greg Brockman ◽  
Bill Kay ◽  
Emma E. Snively
Keyword(s):  
Directed Graphs ◽  
Simple Graphs ◽  
Combinatorial Objects ◽  
Labeled Graphs ◽  
Uniform Hypergraphs ◽  
Universal Cycles ◽  
Multiple Edges

A universal cycle is a compact listing of a class of combinatorial objects. In this paper, we prove the existence of universal cycles of classes of labeled graphs, including simple graphs, trees, graphs with $m$ edges, graphs with loops, graphs with multiple edges (with up to $m$ duplications of each edge), directed graphs, hypergraphs, and $k$-uniform hypergraphs.

scholarly journals Universal Cycles for Weak Orders

2013 ◽  
Vol 27 (3) ◽  
pp. 1360-1371 ◽  
Author(s):  
Victoria Horan ◽  
Glenn Hurlbert
Keyword(s):  
Universal Cycles ◽  
Weak Orders

Products of Universal Cycles

2008 ◽  
pp. 35-55 ◽  
Author(s):  
Persi Diaconis ◽  
Ron Graham
Keyword(s):  
Universal Cycles

scholarly journals Designing locally maximally entangled quantum states with arbitrary local symmetries

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 450
Author(s):  
Oskar Słowik ◽  
Adam Sawicki ◽  
Tomasz Maciążek
Keyword(s):  
Quantum State ◽  
Quantum States ◽  
Local Mode ◽  
Trivial Representation ◽  
Tensor Power ◽  
Technical Result ◽  
Combinatorial Objects ◽  
Local Symmetries ◽  
Entangled Quantum States ◽  
Group Of Symmetries

One of the key ingredients of many LOCC protocols in quantum information is a multiparticle (locally) maximally entangled quantum state, aka a critical state, that possesses local symmetries. We show how to design critical states with arbitrarily large local unitary symmetry. We explain that such states can be realised in a quantum system of distinguishable traps with bosons or fermions occupying a finite number of modes. Then, local symmetries of the designed quantum state are equal to the unitary group of local mode operations acting diagonally on all traps. Therefore, such a group of symmetries is naturally protected against errors that occur in a physical realisation of mode operators. We also link our results with the existence of so-called strictly semistable states with particular asymptotic diagonal symmetries. Our main technical result states that the Nth tensor power of any irreducible representation of SU(N) contains a copy of the trivial representation. This is established via a direct combinatorial analysis of Littlewood-Richardson rules utilising certain combinatorial objects which we call telescopes.

scholarly journals Corners in Tree-Like Tableaux

10.37236/5712 ◽  
2016 ◽  
Vol 23 (4) ◽  
Author(s):  
Paweł Hitczenko ◽  
Amanda Lohss
Keyword(s):  
Exclusion Process ◽  
Limiting Distribution ◽  
Tree Structure ◽  
Random Tree ◽  
Type B ◽  
Combinatorial Objects ◽  
Simple Exclusion Process ◽  
Asymmetric Simple Exclusion ◽  
Simple Exclusion ◽  
Symmetric Tree

In this paper, we study tree–like tableaux, combinatorial objects which exhibit a natural tree structure and are connected to the partially asymmetric simple exclusion process (PASEP). There was a conjecture made on the total number of corners in tree–like tableaux and the total number of corners in symmetric tree–like tableaux. In this paper, we prove both conjectures. Our proofs are based off of the bijection with permutation tableaux or type–B permutation tableaux and consequently, we also prove results for these tableaux. In addition, we derive the limiting distribution of the number of occupied corners in random tree–like tableaux and random symmetric tree–like tableaux.

A SURVEY OF FACTORIZATION COUNTING FUNCTIONS

2005 ◽  
Vol 01 (04) ◽  
pp. 563-581 ◽  
Author(s):  
A. KNOPFMACHER ◽  
M. E. MAYS
Keyword(s):  
Number Theory ◽  
Positive Integer ◽  
Additive Number Theory ◽  
Recursive Algorithms ◽  
Additive Number ◽  
Combinatorial Objects ◽  
Survey Techniques ◽  
Counting Functions ◽  
General Field ◽  
Positive Integers

The general field of additive number theory considers questions concerning representations of a given positive integer n as a sum of other integers. In particular, partitions treat the sums as unordered combinatorial objects, and compositions treat the sums as ordered. Sometimes the sums are restricted, so that, for example, the summands are distinct, or relatively prime, or all congruent to ±1 modulo 5. In this paper we review work on analogous problems concerning representations of n as a product of positive integers. We survey techniques for enumerating product representations both in the unrestricted case and in the case when the factors are required to be distinct, and both when the product representations are considered as ordered objects and when they are unordered. We offer some new identities and observations for these and related counting functions and derive some new recursive algorithms to generate lists of factorizations with restrictions of various types.

Sign in / Sign up

Export Citation Format

Share Document