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On posets of m-ary words

1996
*
Discrete Mathematics
*

f8

doi:10.1016/0012-365x(94)00256-i
fatcat:nqrweouup5dxpihhbscm3m6rbi
*m*• n , which consists*of*the naturally ordered subwords ofthe cyclic*word**on*length n*on*an alphabet*of**m*letters, where subwords are obtained by deleting letters, is introduced and studied. ... This*poset*is*of*special interest since it is strongly related to several different structured*posets*, like Boolean lattices, chains, Higman orders and Kruskal-Katona*posets*. ... The partially ordered set*of*all subwords*of*the*m*-*ary**word*Um,n,i = i (i + l)(i + 2) ... ...##
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Counting smaller elements in the Tamari and m-Tamari lattices
[article]

2015
*
arXiv
*
pre-print

We explain how the

arXiv:1311.3922v2
fatcat:dhnxcm243rbwzgn4sqeycmgjiu
*m*-Tamari lattices can be interpreted in terms*of**m*+1-*ary*trees or a certain class*of*binary trees. ... We then use the interval-*posets*to recover the functional equation*of**m*-Tamari intervals and to prove a generalized formula that counts the number*of*elements smaller than or equal to a given tree in the ... The number*of*nodes*on*the border*of*a*m*-binary tree is the same as*on*its associated (*m*+ 1)-*ary*tree and still corresponds to the number*of*touch points*of*the*m*-ballot path. ...##
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On a quasi-ordering on Boolean functions
[article]

2006
*
arXiv
*
pre-print

It was proved few years ago that classes

arXiv:math/0601218v1
fatcat:7rlvchzr4bgg7gt5cl5vlhcvee
*of*Boolean functions definable by means*of*functional equations EFHH, or equivalently, by means*of*relational constraints Pi2, coincide with initial segments*of*... the quasi-ordered set (Ω, ≤) made*of*the set Ω*of*Boolean functions, suitably quasi-ordered. ... If f is an n-*ary*Boolean function and g 1 , . . . , g n are*m*-*ary*Boolean functions, then their composition is the*m*-*ary*Boolean function f (g 1 , . . . , g n ), whose value*on*every a ∈ B*m*is f (g 1 ...##
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The Number of Irreducible Polynomials and Lyndon Words with Given Trace

2001
*
SIAM Journal on Discrete Mathematics
*

This same approach is used to count Lq(n, t), the number

doi:10.1137/s0895480100368050
fatcat:5zxbulwp4bhbhhits4wrzdoeby
*of*q-*ary*Lyndon*words*whose characters sum to t mod q. ... This number is given by Lq(n, t) = ( gcd(d, q)µ(d)q n/d )/(qn), where the sum is over all divisors d*of*n for which gcd(d, q)|t. Both results rely*on*a new form*of*Möbius inversion. ... Let L q (n, t) denote the number*of*q-*ary*Lyndon*words**of*length n and trace t mod q. ...##
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Symmetric chain decomposition of necklace posets
[article]

2012
*
arXiv
*
pre-print

A finite ranked

arXiv:1104.4147v3
fatcat:4uyk4ryknfbejdz4tah5gccfwq
*poset*is called a symmetric chain order if it can be written as a disjoint union*of*rank-symmetric, saturated chains. ... If P is any symmetric chain order, we prove that P^n/Z_n is also a symmetric chain order, where Z_n acts*on*P^n by cyclic permutation*of*the factors. ... I would like to thank the Department*of*Mathematics at Michigan State University for their hospitality. I am especially grateful to Bruce Sagan for his encouragement while this project was under way. ...##
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Proofs of Conjectures about Pattern-Avoiding Linear Extensions

2019
*
Discrete Mathematics & Theoretical Computer Science
*

After fixing a canonical ordering (or labeling)

doi:10.23638/dmtcs-21-4-16
fatcat:vtacnwc5hjfzjl5owlhssfannm
*of*the elements*of*a finite*poset*,*one*can associate each linear extension*of*the*poset*with a permutation. ... We first consider pattern avoidance in k-*ary*heaps, where we obtain a general result that proves a conjecture*of*Levin, Pudwell, Riehl, and Sandberg in a special case. ... Associating complete k-*ary*trees with*posets*in the natural way,*one*can view a k-*ary*heap as a linear extension*of*the underlying complete k-*ary*tree. ...##
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Symmetric Chain Decomposition of Necklace Posets

2012
*
Electronic Journal of Combinatorics
*

A finite ranked

doi:10.37236/1178
fatcat:6zygtjsbfvcgljo2wabo53g5hq
*poset*is called a symmetric chain order if it can be written as a disjoint union*of*rank-symmetric, saturated chains. ... If $\mathcal{P}$ is any symmetric chain order, we prove that $\mathcal{P}^n/\mathbb{Z}_n$ is also a symmetric chain order, where $\mathbb{Z}_n$ acts*on*$\mathcal{P}^n$ by cyclic permutation*of*the factors ... I would like to thank the Department*of*Mathematics at Michigan State University for their hospitality. I am especially grateful to Bruce Sagan for his encouragement while this project was under way. ...##
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Proofs of Conjectures about Pattern-Avoiding Linear Extensions
[article]

2019
*
arXiv
*
pre-print

After fixing a canonical ordering (or labeling)

arXiv:1905.02309v3
fatcat:z63ffcjibzf2hd5j74n67moz3a
*of*the elements*of*a finite*poset*,*one*can associate each linear extension*of*the*poset*with a permutation. ... We first consider pattern avoidance in k-*ary*heaps, where we obtain a general result that proves a conjecture*of*Levin, Pudwell, Riehl, and Sandberg in a special case. ... Associating complete k-*ary*trees with*posets*in the natural way,*one*can view a k-*ary*heap as a linear extension*of*the underlying complete k-*ary*tree. ...##
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On natural join of posets properties and first applications
[article]

2009
*
arXiv
*
pre-print

In addition to the three standard operations

arXiv:0908.1375v2
fatcat:hgpyzy5hyvaxhaujmx7ktobmn4
*on**posets*which are dual*of**poset*or ordinal and cardinal sums*of*partial ordered sets*one*adds the natural join*of**posets*. ... with posing some questions arising*on*the way. ... and reliable Teacher before she as Independent Person was fired by local Bialystok University local authorities exactly*on*the day she had defended Rota and cobweb*posets*related dissertation with distinction ...##
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On polymorphism-homogeneous relational structures and their clones

2014
*
Algebra Universalis
*

Eventually, we completely characterize the countable polymorphism-homogeneous graphs, the polymorphism-homogeneous

doi:10.1007/s00012-014-0310-3
fatcat:mx6av4chwjgupaoxxum5wzdqri
*posets**of*arbitrary size, and the countable polymorphism-homogeneous strict*posets*. ... polymorphism*of*the structure. ... Let A be a countable set and let L be a meet-complete sublattice*of*E(A). Then L is polymorphism-homogeneous if and only if it is arithmetical. ...##
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The Complexity of the Extendibility Problem for Finite Posets

2003
*
SIAM Journal on Discrete Mathematics
*

In other

doi:10.1137/s0895480101389478
fatcat:xp7jwwgsdzf4rezneeknsymo2y
*words*, if a*poset*admits a near unanimity operation, it also admits a totally symmetric idempotent operation*of*any arity. In [Fund. ... We generalize Pratt and Tiuryn's result*on*crowns by proving that EXT(P ), is NP-complete for any finite*poset*P which admits no nontrivial idempotent Malcev condition. ... The authors would like to thank Pavol Hell for patiently mediating between the referee*of*the paper and the authors. ...##
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Pattern occurrences in k-ary words revisited: a few new and old observations
[article]

2022
*
arXiv
*
pre-print

In this paper, we study the pattern occurrence in k-

arXiv:2102.00443v4
fatcat:xn6hxurzrzd73ny3ndbkplz7nm
*ary**words*. We prove an explicit upper bound*on*the number*of*k-*ary**words*avoiding any given pattern using a random walk argument. ... A simple consequence*of*this connection is that Wilf-equivalence*of*two patterns in*words*implies their Wilf-equivalence in permutations. ... We also would to thank Zachary Hunter for pointing out a gap in the proof*of*Theorem 1.1 in an earlier draft*of*this paper. ...##
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Algebraic and graph-theoretic properties of infiniten-posets

2005
*
RAIRO - Theoretical Informatics and Applications
*

The collection

doi:10.1051/ita:2005018
fatcat:r7ws2sojyvck7gmz2gd2wwtaja
*of*all Σ-labeled n-*posets*is naturally equipped with n binary product operations and n ω-*ary*product operations. ... We show that those Σ-labeled n-*posets*that can be generated from the singletons by the binary and ω-*ary*product operations form the free algebra*on*Σ in a variety axiomatizable by an infinite collection ...*Poset*, n-*poset*, composition, free algebra, equational logic. automata*on*ω-*words*, Perrin and Pin [15, 16] proposed to use free ω-semigroups, which are a two-sorted generalization*of*semigroups and possess ...##
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On a quasi-ordering on Boolean functions

2008
*
Theoretical Computer Science
*

Galois theory for minors

doi:10.1016/j.tcs.2008.01.025
fatcat:2yxiscdhqjajppihu3znqrtpsm
*of*finite functions, Discrete Mathematics 254 (2002) 405-419], coincide with initial segments*of*the quasi-ordered set (Ω , ≤) made*of*the set Ω*of*Boolean functions, suitably ... Looking at examples*of*finitely definable classes, we show that the classes*of*Boolean functions with a bounded number*of*essential variables are finitely definable. ... Acknowledgments The authors would like to thank Arto Salomaa for sending a copy*of*the paper [19] , which provided the optimal lower bound given in (2)*of*Lemma 4. ...##
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Two-element structures modulo primitive positive constructability
[article]

2020
*
arXiv
*
pre-print

In this paper, we give a complete description

arXiv:1905.12333v2
fatcat:jrawdcd5gjbrvcfnfl47vh4eze
*of*the restriction P_Boole*of*P_fin to relational structures*on*a two-element set; in particular, we prove that P_Boole is a lattice. ... Let P_fin be the*poset*which arises from ordering all finite relational structures by pp-constructability. This*poset*is infinite, but we do not know whether it is uncountable. ... In other*words*, we require that there is exactly*one*occurrence*of*a function symbol*on*both sides*of*the equality. The use*of*nested terms is forbidden. ...
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