Log-concavity of the overpartition functiondoi:10.1007/S11139-015-9762-0Benjamin EngelSpringer USB. Engel, Log-concavity of the overpartition function, Ramanujan J. 43 (2) (2017) 229-241.
r-log-concavityPartition functionHardy-Ramanujan-Rademacher formulaLet be the operator given by . A sequence is called asymptotically r-log-concave if are non-negative sequences for and some integer N. Let p(n) be the number of integer partitions of n. We prove that the sequence is ...
q-log concavityDelannoy numbersOverpartitionsIn a previous paper, we studied an overpartition analogue of Gaussian polynomials as the generating function for overpartitions fitting inside an m x n rectangle. Here, we add one more parameter counting the number of overlined parts, obtaining a two-...
Over-(qt)-binomial coefficientFinite versions of q-series identitiesCombinatorial proofsq-log concavityDelannoy numbersOverpartitionsIn a previous paper, we studied an overpartition aJournal of Combinatorial Theory - Series Adoi:10.1016/j.jcta.2018.03.011Dousse...
We bound the mean field approximation for the log partition function |$\\log \\int e^{f(x)}dx$| in terms of |$\\sum _{i eq j}\\mathbb {E}_{Q^{*}}|\\partial _{ij}f|^{2}$| , for a semi-explicit probability measure |$Q^{*}$| characterized as the unique mean field ...
Then, by constructing involutions, we obtain an identity involving a finite theta function and prove the (q,t) ( q , t ) mathContainer Loading Mathjax -log concavity of [ m + n n ] q , t mathContainer Loading Mathjax . We particularly emphasize the role of combinatorial proofs and ...