$(s,t)$-Cores: a Weighted Version of Armstrong’s Conjecture
نویسندگان
چکیده
منابع مشابه
(s, t)-Cores: a Weighted Version of Armstrong's Conjecture
The study of core partitions has been very active in recent years, with the study of ps, tq-cores – partitions which are both sand t-cores – playing a prominent role. A conjecture of Armstrong, proved recently by Johnson, says that the average size of an ps, tq-core, when s and t are coprime positive integers, is 1 24ps ́1qpt ́1qps` t ́1q. Armstrong also conjectured that the same formula gives the...
متن کاملA Version of the Volume Conjecture
Abstract. We propose a version of the volume conjecture that would relate a certain limit of the colored Jones polynomials of a knot to the volume function defined by a representation of the fundamental group of the knot complement to the special linear group of degree two over complex numbers. We also confirm the conjecture for the figure-eight knot and torus knots. This version is different f...
متن کاملA Combinatorial Version of the Grothendieck Conjecture
We study the “combinatorial anabelian geometry” that governs the relationship between the dual semi-graph of a pointed stable curve and various associated profinite fundamental groups of the pointed stable curve. Although many results of this type have been obtained previously in various particular situations of interest under unnecessarily strong hypotheses, the goal of the present paper is to...
متن کاملA Superlocal Version of Reed's Conjecture
Reed’s well-known ω, ∆, χ conjecture proposes that every graph satisfies χ ≤ ⌈ 1 2 (∆ + 1 + ω)⌉. The second author formulated a local strengthening of this conjecture that considers a bound supplied by the neighbourhood of a single vertex. Following the idea that the chromatic number cannot be greatly affected by any particular stable set of vertices, we propose a further strengthening that con...
متن کاملA componentwise version of Terao’s conjecture
We show that the free hyperplane arrangements form a Zariski-closed set in various parameter spaces. Given a geometric lattice L let V(L) be the parameter space of arrangements with intersection lattice isomorphic to L. Coupling our result with a theorem of Yuzvinsky, we conclude that in V(L) the free arrangements are parameterized by a union of connected components of V(L).
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2016
ISSN: 1077-8926
DOI: 10.37236/6161