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1. A direct proof of well-definedness for the polymatroid Tutte polynomial NSTL国家科技图书文献中心

Guan, Xiaxia | Jin, Xian'an - 《Advances in Applied Mathematics》 - 2025,163(Pt.B) - 共18页

摘要：. (2022) [1] introduced the polymatroid Tutte polynomial | ], which generalizes the classical Tutte* polynomial from* | -definedness of the Tutte* polynomial defined by the summation* | another polynomial* that only depends on P. In this paper* | proof of the well-definedness of the polymatroid Tutte

关键词： Tutte polynomial | Polymatroid | Well-definedness

2. A note on the lacking polynomial of the complete bipartite graph NSTL国家科技图书文献中心

Alofi, Amal | Dukes, Mark - 《Discrete mathematics》 - 2025,348(2) - 共8页

摘要： closely related to the Tutte* polynomial of a graph. It* | The lacking polynomial is a graph polynomial | polynomial of the complete bipartite graph. We classify the | introduced by Chan, Marckert, and Selig in 2013 that is | arose by way of a generalization of the Abelian

关键词： Graph polynomial | Sandpile model | Classification problem | Lacking polynomial | Complete bipartite graph | Log-concavity

3. Finitary Affine Oriented Matroids NSTL国家科技图书文献中心

Delucchi, Emanuele | Knauer, Kolja - 《Discrete & computational geometry》 - 2025,73(1) - 208～257 - 共50页

摘要： include applications of the multiplicity Tutte | polynomial of group actions of semimatroids, generalizing | We initiate the axiomatic study of affine | oriented matroids (AOMs) on arbitrary ground sets | , obtaining fundamental notions such as minors

关键词： Affine oriented matroids | Semimatroids | Finitary and toric arrangements

4. On the polymatroid Tutte polynomial NSTL国家科技图书文献中心

Guan, Xiaxia | Yang, Weiling ... - 《Journal of Combinatorial Theory, Series A》 - 2024,201 - ARTN 105798～ - 共14页

摘要：The Tutte* polynomial is a well-studied* | invariant of matroids. The polymatroid Tutte* polynomial TP* | Postnikov, is an extension of the classical Tutte | polynomial from matroids to polymatroids P. In this paper | (x, y), introduced by Bernardi, Kalman, and

关键词： Interpolating behavior | Tutte polynomial | Polymatroid | High-order term | ROOT POLYTOPES | INVARIANT | KNOTS

5. On the Compatible Sets Expansion of the Tutte Polynomial NSTL国家科技图书文献中心

Pierson, Laura - 《Annals of combinatorics》 - 2024,28(1) - 33～42 - 共10页

摘要： the Tutte* polynomial of a matroid using the notion* | formula to Las Vergnas's trivariate Tutte* polynomials of* | Kochol [6] gave a new expansion formula for | of compatible sets, and asked how this expansion | relates to the internal-external activities formula

关键词： Tutte polynomial | Matroid perspective | Morphism of matroids | Internal-external activities | MORPHISM

6. Deletion-contraction and the surface Tutte polynomial NSTL国家科技图书文献中心

Moffatt, Iain | Thompson, Maya - 《European journal of combinatorics》 - 2024,118 - ARTN 103933～ - 共20页

摘要： coming from the surface Tutte polynomial, a polynomial | definition of the surface Tutte* polynomial and recursion* | topological Tutte* polynomials. The first family is that* | . The second family arises from the canonical Tutte | In this paper we unify two families of

关键词： GRAPHS | INVARIANTS

7. Convolution formulas for multivariate arithmetic Tutte polynomials NSTL国家科技图书文献中心

Ma T. | Jin X.... - 《Advances in Applied Mathematics》 - 2024,157 - 共5页

摘要： arithmetic Tutte* polynomial of arithmetic matroids is a* | generalization of the multivariate Tutte* polynomial of matroids* | the multivariate arithmetic Tutte* polynomial of the* | convolution formulas for the multivariate arithmetic Tutte | polynomial of an arithmetic matroid are obtained. Applying

关键词： Arithmetic matroid | Convolution formula | Matroid | Multivariate Tutte polynomial

8. The Merino-Welsh conjecture is false for matroids NSTL国家科技图书文献中心

Beke, Csongor | Csaji, Gergely Kal ... - 《Advances in Mathematics》 - 2024,446 - ARTN 109674～ - 共10页

摘要： conjecture states that the Tutte* polynomial T (M) ( x, y* | The matroidal version of the Merino-Welsh | ) of any matroid M without loops and coloops | satisfies that max( T (M) (2, 0), T (M) (0, 2)) ,,>=. T- M | (1, 1). Equivalently, if the Merino-Welsh

关键词： Tutte polynomial | Merino-Welsh conjecture | SPANNING-TREES | TUTTE | ORIENTATIONS | INEQUALITY

9. Approximating the chromatic polynomial is as hard as computing it exactly NSTL国家科技图书文献中心

Ferenc Bencs | Jeroen Huijben ... - 《Computational complexity》 - 2024,33(1) - 1.1～1.47 - 共47页

摘要： chromatic polynomial* evaluated at q on planar graphs. This* | that a polynomial* time algorithm for approximately* | computing the chromatic polynomial* of a planar graph at* | ) leads to a polynomial* time algorithm for exactly* | , a well-known reparametrization of the Tutte

关键词： #P-hardness | approximate counting | chromatic polynomial | planar graphs | Tutte polynomial

10. Tutte polynomials for some chemical polycyclic graphs NSTL国家科技图书文献中心

Chen, Hanlin - 《Journal of mathematical chemistry》 - 2024,62(10) - 2625～2650 - 共26页

摘要：The Tutte polynomial is a classical polynomial | focus on the Tutte* polynomials for typical silicate* | graph invariant that provides important information | about the structure of a graph. In this study, we | molecular networks and benzenoid systems, and derive exact

关键词： Tutte polynomial | Polymatroid | Well-definedness

摘要： closely related to the Tutte* polynomial of a graph. It* | The lacking polynomial is a graph polynomial | polynomial of the complete bipartite graph. We classify the | introduced by Chan, Marckert, and Selig in 2013 that is | arose by way of a generalization of the Abelian

关键词： Graph polynomial | Sandpile model | Classification problem | Lacking polynomial | Complete bipartite graph | Log-concavity

摘要： include applications of the multiplicity Tutte | polynomial of group actions of semimatroids, generalizing | We initiate the axiomatic study of affine | oriented matroids (AOMs) on arbitrary ground sets | , obtaining fundamental notions such as minors

关键词： Affine oriented matroids | Semimatroids | Finitary and toric arrangements

摘要：The Tutte* polynomial is a well-studied* | invariant of matroids. The polymatroid Tutte* polynomial TP* | Postnikov, is an extension of the classical Tutte | polynomial from matroids to polymatroids P. In this paper | (x, y), introduced by Bernardi, Kalman, and

关键词： Interpolating behavior | Tutte polynomial | Polymatroid | High-order term | ROOT POLYTOPES | INVARIANT | KNOTS

摘要： the Tutte* polynomial of a matroid using the notion* | formula to Las Vergnas's trivariate Tutte* polynomials of* | Kochol [6] gave a new expansion formula for | of compatible sets, and asked how this expansion | relates to the internal-external activities formula

关键词： Tutte polynomial | Matroid perspective | Morphism of matroids | Internal-external activities | MORPHISM

摘要： coming from the surface Tutte polynomial, a polynomial | definition of the surface Tutte* polynomial and recursion* | topological Tutte* polynomials. The first family is that* | . The second family arises from the canonical Tutte | In this paper we unify two families of

关键词： GRAPHS | INVARIANTS

关键词： Arithmetic matroid | Convolution formula | Matroid | Multivariate Tutte polynomial

摘要： conjecture states that the Tutte* polynomial T (M) ( x, y* | The matroidal version of the Merino-Welsh | ) of any matroid M without loops and coloops | satisfies that max( T (M) (2, 0), T (M) (0, 2)) ,,>=. T- M | (1, 1). Equivalently, if the Merino-Welsh

关键词： Tutte polynomial | Merino-Welsh conjecture | SPANNING-TREES | TUTTE | ORIENTATIONS | INEQUALITY

摘要： chromatic polynomial* evaluated at q on planar graphs. This* | that a polynomial* time algorithm for approximately* | computing the chromatic polynomial* of a planar graph at* | ) leads to a polynomial* time algorithm for exactly* | , a well-known reparametrization of the Tutte

关键词： #P-hardness | approximate counting | chromatic polynomial | planar graphs | Tutte polynomial

摘要：The Tutte polynomial is a classical polynomial | focus on the Tutte* polynomials for typical silicate* | graph invariant that provides important information | about the structure of a graph. In this study, we | molecular networks and benzenoid systems, and derive exact

关键词： Tutte polynomial | Benzenoid system | Silicate network | Spanning tree

4008-161-200 800-990-8900

国家科技图书文献中心

关键词： Tutte polynomial | Polymatroid | Well-definedness

摘要： closely related to the Tutte polynomial of a graph. It | The lacking polynomial is a graph polynomial | polynomial of the complete bipartite graph. We classify the | introduced by Chan, Marckert, and Selig in 2013 that is | arose by way of a generalization of the Abelian

关键词： Graph polynomial | Sandpile model | Classification problem | Lacking polynomial | Complete bipartite graph | Log-concavity

摘要： include applications of the multiplicity Tutte | polynomial of group actions of semimatroids, generalizing | We initiate the axiomatic study of affine | oriented matroids (AOMs) on arbitrary ground sets | , obtaining fundamental notions such as minors

关键词： Affine oriented matroids | Semimatroids | Finitary and toric arrangements

摘要：The Tutte polynomial is a well-studied | invariant of matroids. The polymatroid Tutte polynomial TP | Postnikov, is an extension of the classical Tutte | polynomial from matroids to polymatroids P. In this paper | (x, y), introduced by Bernardi, Kalman, and

关键词： Interpolating behavior | Tutte polynomial | Polymatroid | High-order term | ROOT POLYTOPES | INVARIANT | KNOTS

摘要： the Tutte polynomial of a matroid using the notion | formula to Las Vergnas's trivariate Tutte polynomials of | Kochol [6] gave a new expansion formula for | of compatible sets, and asked how this expansion | relates to the internal-external activities formula

关键词： Tutte polynomial | Matroid perspective | Morphism of matroids | Internal-external activities | MORPHISM

摘要： coming from the surface Tutte polynomial, a polynomial | definition of the surface Tutte polynomial and recursion | topological Tutte polynomials. The first family is that | . The second family arises from the canonical Tutte | In this paper we unify two families of

关键词： GRAPHS | INVARIANTS

关键词： Arithmetic matroid | Convolution formula | Matroid | Multivariate Tutte polynomial

摘要： conjecture states that the Tutte polynomial T (M) ( x, y | The matroidal version of the Merino-Welsh | ) of any matroid M without loops and coloops | satisfies that max( T (M) (2, 0), T (M) (0, 2)) ,,>=. T- M | (1, 1). Equivalently, if the Merino-Welsh

关键词： Tutte polynomial | Merino-Welsh conjecture | SPANNING-TREES | TUTTE | ORIENTATIONS | INEQUALITY

摘要： chromatic polynomial evaluated at q on planar graphs. This | that a polynomial time algorithm for approximately | computing the chromatic polynomial of a planar graph at | ) leads to a polynomial time algorithm for exactly | , a well-known reparametrization of the Tutte

关键词： #P-hardness | approximate counting | chromatic polynomial | planar graphs | Tutte polynomial

摘要：The Tutte polynomial is a classical polynomial | focus on the Tutte polynomials for typical silicate | graph invariant that provides important information | about the structure of a graph. In this study, we | molecular networks and benzenoid systems, and derive exact

关键词： Tutte polynomial | Benzenoid system | Silicate network | Spanning tree

4008-161-200 800-990-8900

国家科技图书文献中心

摘要： closely related to the Tutte* polynomial of a graph. It* | The lacking polynomial is a graph polynomial | polynomial of the complete bipartite graph. We classify the | introduced by Chan, Marckert, and Selig in 2013 that is | arose by way of a generalization of the Abelian

摘要：The Tutte* polynomial is a well-studied* | invariant of matroids. The polymatroid Tutte* polynomial TP* | Postnikov, is an extension of the classical Tutte | polynomial from matroids to polymatroids P. In this paper | (x, y), introduced by Bernardi, Kalman, and

摘要： the Tutte* polynomial of a matroid using the notion* | formula to Las Vergnas's trivariate Tutte* polynomials of* | Kochol [6] gave a new expansion formula for | of compatible sets, and asked how this expansion | relates to the internal-external activities formula

摘要： coming from the surface Tutte polynomial, a polynomial | definition of the surface Tutte* polynomial and recursion* | topological Tutte* polynomials. The first family is that* | . The second family arises from the canonical Tutte | In this paper we unify two families of

摘要： conjecture states that the Tutte* polynomial T (M) ( x, y* | The matroidal version of the Merino-Welsh | ) of any matroid M without loops and coloops | satisfies that max( T (M) (2, 0), T (M) (0, 2)) ,,>=. T- M | (1, 1). Equivalently, if the Merino-Welsh

摘要： chromatic polynomial* evaluated at q on planar graphs. This* | that a polynomial* time algorithm for approximately* | computing the chromatic polynomial* of a planar graph at* | ) leads to a polynomial* time algorithm for exactly* | , a well-known reparametrization of the Tutte

摘要：The Tutte polynomial is a classical polynomial | focus on the Tutte* polynomials for typical silicate* | graph invariant that provides important information | about the structure of a graph. In this study, we | molecular networks and benzenoid systems, and derive exact