Do you want to publish a course? Click here

Hall sets, Lazard sets and comma-free codes

95   0   0.0 ( 0 )
 Added by Dominique Perrin
 Publication date 2016
  fields
and research's language is English




Ask ChatGPT about the research

We investigate the relationship between two constructions of maximal comma-free codes described respectively by Eastman and by Scholtz and the notions of Hall sets and Lazard sets introduced in connection with factorizations of free monoids and bases of free Lie algebras.



rate research

Read More

In this paper, we study product-free subsets of the free semigroup over a finite alphabet $A$. We prove that the maximum density of a product-free subset of the free semigroup over $A$, with respect to the natural measure that assigns a weight of $|A|^{-n}$ to each word of length $n$, is precisely $1/2$.
We show that, in contrast to the integers setting, almost all even order abelian groups $G$ have exponentially fewer maximal sum-free sets than $2^{mu(G)/2}$, where $mu(G)$ denotes the size of a largest sum-free set in $G$. This confirms a conjecture of Balogh, Liu, Sharifzadeh and Treglown.
93 - Xiaoyu He , Jiaxi Nie , Sam Spiro 2021
Nielsen proved that the maximum number of maximal independent sets (MISs) of size $k$ in an $n$-vertex graph is asymptotic to $(n/k)^k$, with the extremal construction a disjoint union of $k$ cliques with sizes as close to $n/k$ as possible. In this paper we study how many MISs of size $k$ an $n$-vertex graph $G$ can have if $G$ does not contain a clique $K_t$. We prove for all fixed $k$ and $t$ that there exist such graphs with $n^{lfloorfrac{(t-2)k}{t-1}rfloor-o(1)}$ MISs of size $k$ by utilizing recent work of Gowers and B. Janzer on a generalization of the Ruzsa-Szemeredi problem. We prove that this bound is essentially best possible for triangle-free graphs when $kle 4$.
Strongly walk-regular graphs can be constructed as coset graphs of the duals of projective three-weight codes whose weights satisfy a certain equation. We provide classifications of the feasible parameters in the binary and ternary case for medium size code lengths. Additionally some theoretical insights on the properties of the feasible parameters are presented.
89 - Imed Zaguia 2020
An $alpha$-greedy balanced pair in an ordered set $P=(V,leq)$ is a pair $(x,y)$ of elements of $V$ such that the proportion of greedy linear extensions of $P$ that put $x$ before $y$ among all greedy linear extensions is in the real interval $[alpha, 1-alpha]$. We prove that every $N$-free ordered set which is not totally ordered has a $frac{1}{2}$-greedy balanced pair.
comments
Fetching comments Fetching comments
Sign in to be able to follow your search criteria
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا