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1. Trianguloids and triangulations of root polytopes NSTL国家科技图书文献中心

Galashin, Pavel | Nenashev, Gleb ... - 《Journal of Combinatorial Theory, Series A》 - 2024,201 - ARTN 105802～ - 共28页

摘要：Triangulations of a product of two simplices | and, more generally, of root polytopes are closely | related to Gelfand-Kapranov-Zelevinsky's theory of | discriminants, to tropical geometry, tropical oriented | matroids, and to generalized permutohedra. We introduce a

关键词： Triangulations of products of | simplices | Root polytopes | Generalized permutohedra | Mixed subdivisions | Tropical geometry | Tropical oriented matroids | Trianguloids | PRODUCTS | ARRANGEMENTS...

2. Further refinements of Wilf-equivalence for patterns of length 4 NSTL国家科技图书文献中心

Zhou, Robin D. P. | Zang, Yongchun ... - 《Journal of Combinatorial Theory, Series A》 - 2024,204 - ARTN 105863～ - 共13页

摘要：In this paper, we construct a bijection | between 3142-avoiding permutations and 3241-avoiding | permutations which proves the equidistribution of five | classical set-valued statistics. Our bijection also | enables us to establish a bijection between 3142avoiding

关键词： Pattern avoidance | Equidistribution | Wilf-equivalence | Set-valued statistic

3. Power-free complementary binary morphisms NSTL国家科技图书文献中心

Shallit, Jeffrey | Shur, Arseny ... - 《Journal of Combinatorial Theory,Series A》 - 2024,207 - 共23页

摘要：We revisit the topic of power-free morphisms | , focusing on the properties of the class of complementary | morphisms. Such morphisms are defined over a 2-letter | alphabet, and map the letters 0 and 1 to complementary | words. We prove that every prefix of the famous Thue

关键词： Combinatorics on words | Power-free word | Power-free morphism

4. On the difference of the enhanced power graph and the power graph of a finite group NSTL国家科技图书文献中心

Biswas, Sucharita | Cameron, Peter J.... - 《Journal of Combinatorial Theory,Series A》 - 2024,208 - 共31页

摘要：The difference graph D ( G ) of a finite group | G is the difference of the enhanced power graph of | G and the power graph of G , where all isolated | vertices are removed. In this paper we study the | connectedness and perfectness of D ( G ) with respect to

关键词： Power graph | Enhanced power graph | Finite group

5. Block-transitive 2-designs with a chain of imprimitive point-partitions NSTL国家科技图书文献中心

Amarra, Carmen | Devillers, Alice ... - 《Journal of Combinatorial Theory, Series A》 - 2024,205 - ARTN 105866～ - 共32页

摘要：More than 30 years ago, Delandtsheer and Doyen | showed that the automorphism group of a block | -transitive 2 -design, with blocks of size k, could leave | invariant a nontrivial pointpartition, but only if the | number of points was bounded in terms of k. Since then

关键词： Block-transitive designs | Point-imprimitive designs | Wreath products of groups | Generalised wreath products | T-DESIGNS

6. Matroid Horn functions NSTL国家科技图书文献中心

Berczi, Kristof | Boros, Endre ... - 《Journal of Combinatorial Theory, Series A》 - 2024,203 - ARTN 105838～ - 共24页

摘要：Hypergraph Horn functions were introduced as a | subclass of Horn functions that can be represented by a | collection of circular implication rules. These functions | possess distinguished structural and computational | properties. In particular, their characterizations in terms

关键词： Boolean minimization | Horn functions | Matroids | Turan systems | REPRESENTATIONS

7. A bivariate Q-polynomial structure for the non-binary Johnson scheme NSTL国家科技图书文献中心

Crampe, Nicolas | Vinet, Luc ... - 《Journal of Combinatorial Theory, Series A》 - 2024,202 - ARTN 105829～ - 共25页

摘要：The notion of multivariate P- and Q-polynomial | association scheme has been introduced recently | , generalizing the wellknown univariate case. Numerous examples | of such association schemes have already been | exhibited. In particular, it has been demonstrated that

关键词： Non-binary Johnson scheme | BivariateQ-polynomial property | Bispectrality | Subconstituent algebra | ORTHOGONAL POLYNOMIALS | ASSOCIATION SCHEMES | SUBCONSTITUENT ALGEBRA

8. On linear diameter perfect Lee codes with distance 6 NSTL国家科技图书文献中心

Zhang, Tao | Ge, Gennian - 《Journal of Combinatorial Theory, Series A》 - 2024,201 - ARTN 105816～ - 共26页

摘要：In 1968, Golomb and Welch conjectured that | there is no perfect Lee codes with radius r >= 2 and | dimension n >= 3. A diameter perfect code is a natural | generalization of the perfect code. In 2011, Etzion (2011) [5 | ] proposed the following problem: Are there diameter

关键词： Diameter perfect code | Lee metric | Group ring | Lattice tiling | Ternary Golay | NONEXISTENCE THEOREMS | ERROR-CORRECTION | TILINGS

9. Flag-transitive automorphism groups of 2-designs with λ ≥ ( r, λ ) 2 are not product type NSTL国家科技图书文献中心

Li, Huiling | Zhang, Zhilin ... - 《Journal of Combinatorial Theory,Series A》 - 2024,208 - 共14页

摘要：In this note we show that a flag -transitive | automorphism group G of a non -trivial 2-(v, k, lambda | ) design with lambda >= (r, lambda) 2 is not of product | action type. In conclusion, G is a primitive group of | affine or almost simple type. (c) 2024 Elsevier Inc

关键词： 2-design | Flag-transitive | Product action

10. Constructing uniform 2-factorizations via row-sum matrices: Solutions to the Hamilton-Waterloo problem NSTL国家科技图书文献中心

Burgess, A. C. | Danziger, P.... - 《Journal of Combinatorial Theory, Series A》 - 2024,201 - ARTN 105803～ - 共26页

摘要：In this paper, we formally introduce the | concept of a row-sum matrix over an arbitrary group G | . When G is cyclic, these types of matrices have been | widely used to build uniform 2-factorizations of small | Cayley graphs (or, Cayley subgraphs of blown-up cycles

关键词： 2-factorizations | Resolvable cycle decompositions | Cycle systems | Generalized Oberwolfach problem | Hamilton-Waterloo problem | Row-sum matrices | OBERWOLFACH PROBLEM | SIZES

摘要：Triangulations of a product of two simplices | and, more generally, of root polytopes are closely | related to Gelfand-Kapranov-Zelevinsky's theory of | discriminants, to tropical geometry, tropical oriented | matroids, and to generalized permutohedra. We introduce a

关键词： Triangulations of products of | simplices | Root polytopes | Generalized permutohedra | Mixed subdivisions | Tropical geometry | Tropical oriented matroids | Trianguloids | PRODUCTS | ARRANGEMENTS...

摘要：In this paper, we construct a bijection | between 3142-avoiding permutations and 3241-avoiding | permutations which proves the equidistribution of five | classical set-valued statistics. Our bijection also | enables us to establish a bijection between 3142avoiding

关键词： Pattern avoidance | Equidistribution | Wilf-equivalence | Set-valued statistic

摘要：We revisit the topic of power-free morphisms | , focusing on the properties of the class of complementary | morphisms. Such morphisms are defined over a 2-letter | alphabet, and map the letters 0 and 1 to complementary | words. We prove that every prefix of the famous Thue

关键词： Combinatorics on words | Power-free word | Power-free morphism

摘要：The difference graph D ( G ) of a finite group | G is the difference of the enhanced power graph of | G and the power graph of G , where all isolated | vertices are removed. In this paper we study the | connectedness and perfectness of D ( G ) with respect to

关键词： Power graph | Enhanced power graph | Finite group

摘要：More than 30 years ago, Delandtsheer and Doyen | showed that the automorphism group of a block | -transitive 2 -design, with blocks of size k, could leave | invariant a nontrivial pointpartition, but only if the | number of points was bounded in terms of k. Since then

关键词： Block-transitive designs | Point-imprimitive designs | Wreath products of groups | Generalised wreath products | T-DESIGNS

摘要：Hypergraph Horn functions were introduced as a | subclass of Horn functions that can be represented by a | collection of circular implication rules. These functions | possess distinguished structural and computational | properties. In particular, their characterizations in terms

关键词： Boolean minimization | Horn functions | Matroids | Turan systems | REPRESENTATIONS

摘要：The notion of multivariate P- and Q-polynomial | association scheme has been introduced recently | , generalizing the wellknown univariate case. Numerous examples | of such association schemes have already been | exhibited. In particular, it has been demonstrated that

关键词： Non-binary Johnson scheme | BivariateQ-polynomial property | Bispectrality | Subconstituent algebra | ORTHOGONAL POLYNOMIALS | ASSOCIATION SCHEMES | SUBCONSTITUENT ALGEBRA

摘要：In 1968, Golomb and Welch conjectured that | there is no perfect Lee codes with radius r >= 2 and | dimension n >= 3. A diameter perfect code is a natural | generalization of the perfect code. In 2011, Etzion (2011) [5 | ] proposed the following problem: Are there diameter

关键词： Diameter perfect code | Lee metric | Group ring | Lattice tiling | Ternary Golay | NONEXISTENCE THEOREMS | ERROR-CORRECTION | TILINGS

摘要：In this note we show that a flag -transitive | automorphism group G of a non -trivial 2-(v, k, lambda | ) design with lambda >= (r, lambda) 2 is not of product | action type. In conclusion, G is a primitive group of | affine or almost simple type. (c) 2024 Elsevier Inc

关键词： 2-design | Flag-transitive | Product action

摘要：In this paper, we formally introduce the | concept of a row-sum matrix over an arbitrary group G | . When G is cyclic, these types of matrices have been | widely used to build uniform 2-factorizations of small | Cayley graphs (or, Cayley subgraphs of blown-up cycles

关键词： 2-factorizations | Resolvable cycle decompositions | Cycle systems | Generalized Oberwolfach problem | Hamilton-Waterloo problem | Row-sum matrices | OBERWOLFACH PROBLEM | SIZES

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