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Describing the equality conditions of the Alexandrov–Fenchel inequality has been a major open problem for decades. We prove that for a natural class of convex polytopes, the equality cases of the AF inequality are not in unless the polynomial hierarchy ...

In this paper, we consider a certain class of inequalities for the partition function of the following form: ∏ i = 1 T p ( n + s i ) ≥ ∏ i = 1 T p ( n + r i ) , which we call multiplicative inequalities. Given a multiplicative inequality with the ...

A newsvendor game allows the players to collaborate on inventory pooling and share the resulting total cost. There are several possible ways to allocate the cost. Previous studies have focused on the core of the game. It is known that the core of the ...

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 combinations of log-concave sequences that have been transformed by convolution ...

We prove conditional negative association for random variables x_j = 1**math-image** (j∈[n]:= {1…n}) , where σ(1)…σ(m) are i.i.d. from [n]. (The σ(i) 's are thought of as the locations of balls dropped independently into urns 1…n according to some common ...

We give counterexamples and a few positive results related to several conjectures of R. Pemantle (Pemantle, J Math Phys 41 (2000), 1371–1390) and D. Wagner (Wagner, Ann Combin 12 (2008), 211–239) concerning negative correlation and log-concavity ...

In this paper, we present a comprehensive study of the monotonicity and log-concavity of the generalized Marcum and Nuttall Q-functions. More precisely, a simple probabilistic method is first given to prove the monotonicity of these two functions. Then, ...

Some entropy comparison results are presented concerning compound distributions on nonnegative integers. The main result shows that, under a log-concavity assumption, two compound distributions are ordered in terms of Shannon entropy if both the "...

A clear understanding of the behavior of error probability (EP) as a function of signal-to-noise ratio (SNR) and other system parameters is fundamental for assessing the design of digital wireless communication systems. We propose an analytical ...

Let P(x) be a polynomial of degree m, with nonnegative and nondecreasing coefficients. We settle the conjecture that for any positive real number d, the coefficients of P(x + d) form a unimodal sequence, of which the special case d being a positive ...

Let f(x) and g(x) be two real polynomials whose leading coefficients have the same sign. Suppose that f(x) and g(x) have only real zeros and that g interfaces f or g alternates left of f. We show that if ad ≥ bc then the polynomial (bx + a)f(x) + (dx + ...