Arrangements Of Minors In The Positive Grassmannian And a Triangulation of The Hypersimplex by Miriam Farber, Yelena Mandelshtam

“…The structure of zero and nonzero minors in the Grassmannian leads to rich combinatorics of matroids. In this paper, we investigate an even richer structure of possible equalities and inequalities between the minors in the positive Grassmannian. …”
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Biadjoint scalar tree amplitudes and intersecting dual associahedra by Hadleigh Frost

“…Abstract We present a new formula for the biadjoint scalar tree amplitudes m(α|β) based on the combinatorics of dual associahedra. Our construction makes essential use of the cones in ‘kinematic space’ introduced by Arkani-Hamed, Bai, He, and Yan. …”
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An Efficient Polynomial Time Approximation Scheme for the Vertex Cover P3 Problem on Planar Graphs by Tu Jianhua, Shi Yongtang

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Abel-Gontcharoff polynomials, parking trajectories and ruin probabilities by Lefèvre Claude, Picard Philippe

“…Then, we extend the remarkable links existing between these polynomials and the parking functions which are a classic object in combinatorics and computer science. Finally, we use the polynomials to determine the non-ruin probabilities over a finite horizon for a bivariate risk process, in discrete and continuous time, assuming that claim amounts are dependent via a partial Schur-constancy property.…”
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Entropies of Weighted Sums in Cyclic Groups and an Application to Polar Codes by Emmanuel Abbe, Jiange Li, Mokshay Madiman

“…These results are closely related to the study of more-sums-than-differences (i.e., MSTD) sets in additive combinatorics. We also investigate polar codes for q-ary input channels using non-canonical kernels to construct the generator matrix and present applications of our results to constructing polar codes with significantly improved error probability compared to the canonical construction.…”
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Quantum computation of discrete logarithms in semigroups by Childs Andrew M., Ivanyos Gábor

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Foundations of Online Structure Theory II: The Operator Approach by Rod Downey, Alexander Melnikov, Keng Meng Ng

“…We give a new framework which (i) ties online algorithms with computable analysis, (ii) shows how to use modifications of notions from computable analysis, such as Weihrauch reducibility, to analyse finite but uniform combinatorics, (iii) show how to finitize reverse mathematics to suggest a fine structure of finite analogs of infinite combinatorial problems, and (iv) see how similar ideas can be amalgamated from areas such as EX-learning, computable analysis, distributed computing and the like. …”
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Biographic Context in V. V. Nabokov’s Novels “Glory” and “Transparent Things” by E. G. Nikolayeva

“…The references in these novels to the works of Russian and foreign literature, to the biographies of writers and poets (“biographical plot”) speak not only about Nabokov’s cultivation of a new plot on the basis of the combinatorics of borrowed plots and their elements, but also about the meta-literary discussion of these plots, biographies and creative experience of predecessors. …”
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On computational properties of gene assembly in ciliates by Vladimir Rogojin

“…Those paradigms contribute in particular to combinatorics, formal languages and computability theories.…”
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Extending the parking space by Andrew Berget, Brendon Rhoades

“…The action of the symmetric group $S_n$ on the set $\mathrm{Park}_n$ of parking functions of size $n$ has received a great deal of attention in algebraic combinatorics. We prove that the action of $S_n$ on $\mathrm{Park}_n$ extends to an action of $S_{n+1}$. …”
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Natural Abundance Isotopic Chirality in the Reagents of the Soai Reaction by Béla Barabás, Róbert Kurdi, Gyula Pályi

“…Therefore magnitude and eventual effects of isotopic chirality caused by natural abundance isotopic substitution (H, C, O, Zn) in the reagents of the Soai reaction were analyzed by combinatorics and probability calculations. Expectable enantiomeric excesses were calculated by the Pars–Mills equation. …”
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A Note on Distance-based Graph Entropies by Zengqiang Chen, Matthias Dehmer, Yongtang Shi

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Constructing Words with High Distinct Square Densities by F. Blanchet-Sadri, S. Osborne

“…Improvements by Ilie to 2n-Θ(log n) and by Deza et al. to 11n/6 rely on the study of combinatorics of FS-double-squares, when the maximum number of two last occurrences of squares begin. …”
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Cubic surfaces and their invariants: Some memories of Raymond Stora by Michel Bauer

“…Each smooth cubic surface has a rich geometric structure, which I review briefly, with emphasis on the 27 lines and the combinatorics of their intersections. Only elementary methods are used, relying on first order perturbation/deformation theory. …”
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On the power of coherently controlled quantum adiabatic evolutions by Mária Kieferová, Nathan Wiebe

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COMBINATORIAL ANALYSIS OF THE DOMINOES SCHEME AND THE CASE OF FIXED MINIMAL FIGURE ON A DOMINO TILE by Natalia Enatskaya

“…This scheme is studied, together with an analogous one,</pre><pre> with a fixed minimal figure <span>$r\ge m$</span> at the outcome of a random choice</pre><pre> of a tile from a complete domino set, using the following ways of enumerative</pre><pre> combinatorics: design of the enumeration procedure for the numbered outcomes of the scheme, determination of their number, solution of the corresponding numeration problem (i.e. establishment of one-to-one correspondence between numbers and types of the outcomes of the scheme), finding of their probabilistic distribution and <span>modeling</span> </pre><pre>of their possible outcomes</pre>…”
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Entropy of Weighted Graphs with Randi´c Weights by Zengqiang Chen, Matthias Dehmer, Frank Emmert-Streib, Yongtang Shi

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List circular backbone colouring by Frederic Havet, Andrew D. King

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New Results on Generalized Graph Coloring by Vladimir E. Alekseev, Alastair Farrugia, Vadim V. Lozin

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The Effect of Indexing on the Complexity of Object Recognition by Grimson, W. Eric L.

“…In this paper, we turn to the problem of selecting models from a library, and examine the combinatorics of determining that a candidate object is not present in the data. …”
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