2 citations · 3 across the 6 of their papers we have counts for
7 papers
The CLLC conjecture holds for cyclic outer permutations
Jonathan L. Gross, Toufik Mansour, Thomas W. Tucker +1
Recently, Gross et al. posed the LLC conjecture for the locally log-concavity of the genus distribution of every graph, and provided an equivalent combinatorial version, the CLLC c…
Root geometry of polynomial sequences II: Type (1,0)
J. L. Gross, T. Mansour, T. W. Tucker +1
We consider the sequence of polynomials defined by the recursion , with initial values and , where $a,b,d,t,…
Root geometry of polynomial sequences I: Type
J. L. Gross, T. Mansour, T. W. Tucker +1
This paper is concerned with the distribution in the complex plane of the roots of a polynomial sequence given by a recursion $W_n(x)=aW_{n-1}(x)+(bx+c)W_{n-2}…
Log-concavity of the genus polynomials of Ringel ladders
J. L. Gross, T. Mansour, T. W. Tucker +1
A Ringel ladder can be formed by a self-bar-amalgamation operation on a symmetric ladder, that is, by joining the root vertices on its end-rungs. The present authors have previousl…
Iterated claws have real-rooted genus polynomials
J. L. Gross, T. Mansour, T. W. Tucker +1
We prove that the genus polynomials of the graphs called iterated claws are real-rooted. This continues our work directed toward the 25-year-old conjecture that the genus distribut…
Genus Distributions of cubic series-parallel graphs
Jonathan L. Gross, Michal Kotrbčík, Timothy Sun
We derive a quadratic-time algorithm for the genus distribution of any 3-regular, biconnected series-parallel graph, which we extend to any biconnected series-parallel graph of max…
Log-Concavity of Combinations of Sequences and Applications to Genus Distributions
Jonathan L. Gross, Toufik Mansour, Thomas W. Tucker +1
We formulate conditions on a set of log-concave sequences, under which any linear combination of those sequences is log-concave, and further, of conditions under which linear combi…